Seminars

By Year

Title: Closed subroot systems of finite and affine root systems.
Speaker: Krishanu Roy (IMSc, Chennai)
Date: 24 November 2017
Time: 10:30 AM
Venue: LH-1, Mathematics Department

In this talk, I will tell you about the Borel-de-Sibenthal theorem which gives the classification of all maximal closed subroot systems of finite crystallographic root systems. I will start my talk by introducing the notion of finite root systems and it’s closed subroot systems.

The concept of root system is very fundamental in the theory of Lie groups and Lie algebras. Especially they play a vital role in the classification of finite dimensional semi-simple Lie algebras. Closed subroot systems of finite root systems naturally appear in the Borel-de-Sibenthal theory which describes the closed connected subgroups of a compact Lie group that have maximal rank. The classification of closed subroot systems is essential in the classification of semi-simple subalgebras of semi-simple Lie algebras.

Through out this talk, we will try to stay within the theory of root systems and reflection groups. No knowledge of Lie algebras or Lie groups will be assumed. If time permits I will discuss about my joint work with R. Venkatesh which gives explicit descriptions of the maximal closed subroot systems of affine root systems.

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Title: Arithmetic geometry of toric varieties.
Speaker: Patrice Philippon (CNRS, Paris)
Date: 22 November 2017
Time: 4:00 pm
Venue: LH-1, Mathematics Department

We will present results obtained in collaboration with J.Burgos and M.Sombra. These extend the well known dictionary between the geometric properties of toric varieties and convex geometry. In particular, we give combinatorial descriptions of classical invariants of arithmetic geometry, such as metric, height or essential minimum.

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Title: Unique factorization property of Schur functions
Speaker: R. Venkatesh (IISc, Bangalore)
Date: 11 November 2017
Time: 3 - 4:55 pm (with a 15 minute break in between)
Venue: LH-1, Mathematics Department

In this talk, we prove the unique factorization property of Schur functions. This fundamental property of Schur functions was first observed and proved by C. S. Rajan in 2004. I give a different proof of this beautiful fact which I jointly obtained with my adviser S. Viswanath. I begin my talk with introducing the Schur functions and its connections with representation theory of general linear groups. Basic knowledge of elementary algebra will be assumed like group theory and linear algebra. If time permits, I will tell you about the possible generalizations of this result.

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Title: Irrational rotations, random affine transformations and the central limit theorem
Speaker: Nishant Chandgotia (Tel Aviv University, Israel)
Date: 09 October 2017
Time: 3 pm
Venue: LH-1, Mathematics Department

It is a well-known result from Hermann Weyl that if alpha is an irrational number in [0,1) then the number of visits of successive multiples of alpha modulo one in an interval contained in [0,1) is proportional to the size of the interval. In this talk we will revisit this problem, now looking at finer joint asymptotics of visits to several intervals with rational end points. We observe that the visit distribution can be modelled using random affine transformations; in the case when the irrational is quadratic we obtain a central limit theorem as well. Not much background in probability will be assumed. This is in joint work with Jon Aaronson and Michael Bromberg.

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Title: The quest for a polynomial that is hard to compute
Speaker: Neeraj Kayal (Microsoft Research, Bangalore)
Date: 06 October 2017
Time: 3 - 4:55 pm (with a 15 minute break in between)
Venue: LH-1, Mathematics Department

We consider the computation of n-variate polynomials over a field F via a sequence of arithmetic operations such as additions, subtractions, multiplications, divisions, etc. It has been known for at five decades now that a random n-variate polynomial of degree n is hard to compute. Yet not a single explicit polynomial is provably known to be hard to compute (although we have a lot of good candidates). In this talk we will first describe this problem and its relationship to the P vs NP problem. We will then describe several partial results on this problem, both old and new, along with a more general approach/framework that ties together most of these partial results.

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Title: Partition of integers :- a treasure trove of open problems : order matching and unimodality
Speaker: N. Narayanan (IIT, Madras)
Date: 06 October 2017
Time: 10:30 am
Venue: LH-1, Mathematics Department

A partition of integer $n$ is a sequence $\lambda = (\lambda_1, \lambda_2, \cdots, \lambda_k, \cdots)$ of non negative integers such that $\lambda_i \ge \lambda_{i+1}$ and $\sum_i \lambda_i = n$. It follows that there are finitely many non-zero $\lambda_i$’s. One can restrict the number of them and the largest value of $\lambda_i$ and observe that the set of such partitions form a poset under a suitable relation. Several natural questions arise in this setting. Some of these questions have been answered by Proctor, Stanley and Kathy O’Hara among others. We take a look at some techniques as given by Stanley and ask if it is possible to extend it to higher dimensions.

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Title: Invertibility and condition number of sparse random matrices
Speaker: Anirban Basak (Weizmann Institute of Science, Israel)
Date: 05 October 2017
Time: 4 pm
Venue: LH-1, Mathematics Department

I will describe our work that establishes (akin to) von Neumann’s conjecture on condition number, the ratio of the largest and the smallest singular values, for sparse random matrices. Non-asymptotic bounds on the extreme singular values of large matrices have numerous uses in the geometric functional analysis, compressed sensing, and numerical linear algebra. The condition number often serves as a measure of stability for matrix algorithms. Based on simulations von Neumann and his collaborators conjectured that the condition number of a random square matrix of dimension $n$ is $O(n)$. During the last decade, this conjecture was proved for dense random matrices.

Sparse matrices are abundant in statistics, neural networks, financial modeling, electrical engineering, and wireless communications. Results for sparse random matrices have been unknown and requires completely new ideas due to the presence of a large number of zeros. We consider a sparse random matrix with entries of the form $\xi_{i,j} \delta_{i,j}, \, i,j=1,\ldots,n$, such that $\xi_{i,j}$ are i.i.d. with zero mean and unit variance and $\delta_{i,j}$ are i.i.d. Ber$(p_n)$, where $p_n \downarrow 0$ as $n \to \infty$. For $p_n < \frac{\log n}{n}$, this matrix becomes non-invertible, and hence its condition number equals infinity, with probability tending to one. In this talk, I will describe our work showing that the condition number of such sparse matrices (under certain assumptions on the moments of $\{\xi_{i,j}\}$) is $O(n^{1+o(1)})$ for all $p_n > \frac{\log n}{n}$, with probability tending to one, thereby establishing the optimal analogous version of the von Neumann’s conjecture on condition number for sparse random matrices.

This talk is based on a sequence of joint works with Mark Rudelson.

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Title: Counting complex solutions of polynomial equations via Newton polytopes
Speaker: Jugal Verma (IIT, Bombay)
Date: 05 September 2017
Time: 2:30 - 3:45 and 4:00 - 5:00 pm
Venue: LH-1, Mathematics Department

We shall discuss a theorem of Bernstein published in 1975 about the number of common solutions of n complex polynomials in n variables in terms of the mixed volumes of their Newton polytopes. This is a far reaching generalisation of the Fundamental Theorem of Algebra and Bezout’s Theorem about intersections of plane algebraic curves. If time permits, we shall sketch a proof of Bernstein’s theorem using Hilbert functions of monomial ideals in polynomial rings.

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Title: Eigenfunctions Seminar: The history of matrix positivity preservers
Speaker: Apoorva Khare (IISc Mathematics)
Date: 18 August 2017
Time: 3 - 4 and 4:15 - 5:15 pm
Venue: LH-1, Mathematics Department

I will give a gentle historical (and ongoing) account of matrix positivity and of operations that preserve it. This is a classical question studied for much of the past century, including by Schur, Polya-Szego, Schoenberg, Kahane, Loewner, and Rudin. It continues to be pursued actively, for both theoretical reasons as well as applications to high-dimensional covariance estimation. I will end with some recent joint work with Terence Tao (UCLA).

The entire talk should be accessible given a basic understanding of linear algebra/matrices and one-variable calculus. That said, I will occasionally insert technical details for the more advanced audience. For example: this journey connects many seemingly distant mathematical topics, from Schur (products and complements), to spheres and Gram matrices, to Toeplitz and Hankel matrices, to rank one updates and Rayleigh quotients, to Cauchy-Binet and Jacobi-Trudi identities, back full circle to Schur (polynomials).

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Title: Quantum Theory of Dark matter
Speaker: Krishna M (Ashoka University)
Date: 09 August 2017
Time: 3:30 pm
Venue: LH-1, Mathematics Department

In this talk we discuss a formulation of Quantum Theory of Dark matter and discuss some operators on Hilbert spaces of singular measures.

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Title: For good measure ... and bad
Speaker: Malabika Pramanik (UBC, Canada)
Date: 02 August 2017
Time: 3:30 pm
Venue: LH-1, Mathematics Department

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Title: The Pick--Nevanlinna interpolation problem: complex-analytic methods in special domains
Speaker: Vikramjit Singh Chandel (IISc Mathematics)
Date: 17 July 2017
Time: 3 pm
Venue: LH-1, Mathematics Department

The Pick–Nevanlinna interpolation problem in its fullest generality is as follows:

Given domains $D_1$, $D_2$ in complex Euclidean spaces, and a set ${(z_i,w_i): 1\leq i\leq N}\subset D_1\times D_2$, where $z_i$ are distinct and $N$ is a positive integer $\geq 2$, find necessary and sufficient conditions for the existence of a holomorphic map $F$ from $D_1$ into $D_2$ such that $F(z_i) = w_i$, $1\leq N$.

When such a map $F$ exists, we say that $F$ is an interpolant of the data. Of course, this problem is intractable at the above level of generality. However, two special cases of the problem – which we shall study in this thesis – have been of lasting interest:

INTERPOLATION FROM THE POLYDISC TO THE UNIT DISC: This is the case $D_1 = D^n$ and $D_2 = D$, where $D$ denotes the open unit disc in the complex plane and $n$ is a positive integer. The problem itself originates with Georg Pick’s well-known theorem (independently discovered by Nevanlinna) for the case $n=1$. Much later, Sarason gave another proof of Pick’s result using an operator-theoretic approach, which is very influential. Using this approach for $n\geq 2$, Agler–McCarthy provided a solution to the problem with the restriction that the interpolant is in the Schur–Agler class. This is notable because when $n = 2$ the latter result completely solves the problem for the case $D_1 = D^2$, $D_2 = D$. However, Pick’s approach can also be effective for $n\geq 2$. In this thesis, we give an alternative characterization for the existence of a $3$-point interpolant based on Pick’s approach and involving the study of rational inner functions.

Cole, Lewis and Wermer lifted Sarason’s approach to uniform algebras – leading to a characterization for the existence of an interpolant in terms of the positivity of a large, rather abstractly-defined family of $(N\times N)$ matrices. McCullough later refined their result by identifying a smaller family of matrices. The second result of this thesis is in the same vein, namely: it provides a characterization of those data that admit a $D^n$-to-$D$ interpolant in terms of the positivity of a family of matrices parametrized by a class of polynomials.

INTERPOLATION FORM THE UNIT DISC TO THE SPECTRAL UNIT BALL: This is the case $D_1 = D$ and $D_2$ is the set of all $(n\times n)$ matrices with spectral radius less than $1$. The interest in this arises from problems in Control Theory. Bercovici, Fois and Tannenbaum adapted Sarason’s methods to give a (somewhat hard-to-check) characterization for the existence of an interpolant under a very mild restriction. Later, Agler–Young established a relation between the interpolation problem in the spectral unit ball and that in the symmetrized polydisc – leading to a necessary condition for the existence of an interpolant. Bharali later provided a new inequivalent necessary condition for the existence of an interpolant for any $n$ and $N=2$. We shall present a necessary condition for the existence of a $3$-point interpolant. This we shall achieve by modifying Pick’s approach and applying the aforementioned result due to Bharali.

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Title: The representation homology of spaces
Speaker: Ajay Ramadoss (Indiana University, USA)
Date: 12 July 2017
Time: 4 pm
Venue: LH-1, Mathematics Department

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Title: Analytic models, dilations, wandering subspaces, and inner functions
Speaker: Monojit Bhattacharjee (IISc Mathematics)
Date: 03 July 2017
Time: 3 pm
Venue: LH-1, Mathematics Department

In this talk we will discuss an analytic model theory for pure hyper- contractions (introduced by J. Agler) which is analogous to Sz.Nagy-Foias model theory for contractions. We then proceed to study analytic model theory for doubly commuting $n$-tuples of operators and analyze the structure of joint shift co-invariant subspaces of reproducing kernel Hilbert spaces over polydisc. In particular, we completely characterize the doubly commuting quotient modules of a large class of reproducing kernel Hilbert Modules, in the sense of Arazy and Englis, over the unit polydisc.

Inspired by Halmos, in the second half of the talk, we will focus on the wandering subspace property of commuting tuples of bounded operators on Hilbert spaces. We prove that for a large class of analytic functional Hilbert spaces $H_k$ on the unit ball in $\mathbb{C}^n$, wandering subspaces for restrictions of the multiplication tuple $M_z = (M_{z_1},…,M_{z_n})$ can be described in terms of suitable $H_k$-inner functions. We also prove that $H_k$-inner functions are contractive multipliers and deduce a result on the multiplier norm of quasi-homogeneous polynomials as an application. Along the way we also prove a refinement of a result of Arveson on the uniqueness of the minimal dilations of pure row contractions.

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Title: Homogeneous Operators
Speaker: Somnath Hazra (IISc Mathematics)
Date: 19 June 2017
Time: 11 am
Venue: LH-1, Mathematics Department

It is known that the characteristic function $\theta_T$ of a homogeneous contraction $T$ with an associated representation $\pi$ is of the form $\theta_T(a) = \sigma_{L}(\phi_a)^{*} \theta(0) \sigma_{R}(\phi_a),$ where, $\sigma_{L}$ and $\sigma_{R}$ are projective representation of the M"{o}bius group M"{o}b with a common multiplier. We give another proof of the “product formula’’.

Also, we prove that the projective representations $\sigma_L$ and $\sigma_R$ for a class of multiplication operators, the two representations $\sigma_{R}$ and $\sigma_{L}$ are unitarily equivalent to certain known pair of representations $\sigma_{\lambda + 1}$ and $\sigma_{\lambda - 1},$ respectively. These are described explicitly.

Let $G$ be either (i) the direct product of $n$-copies of the bi-holomorphic automorphism group of the disc or (ii) the bi-holomorphic automorphism group of the polydisc $\mathbb D^n.$

A commuting tuple of bounded operators $\mathsf{T} = (T_1, T_2,\ldots ,T_n)$ is said to be $G$-homogeneous if the joint spectrum of $\mathsf{T}$ lies in $\overline{\mathbb{D}}^n$ and $\varphi(\mathsf{T}),$ defined using the usual functional calculus, is unitarily equivalent with $\mathsf{T}$ for all $\varphi \in G.$

We show that a commuting tuple $\mathsf{T}$ in the Cowen-Douglas class of rank $1$ is $G$-homogeneous if and only if it is unitarily equivalent to the tuple of the multiplication operators on either the reproducing kernel Hilbert space with reproducing kernel $\prod_{i = 1}^{n} \frac{1}{(1 - z_{i}\overline{w}_{i})^{\lambda_i}}$ or $\prod_{i = 1}^{n} \frac{1}{(1 - z_{i}\overline{w}_{i})^{\lambda}},$ where $\lambda,$ $\lambda_i$, $1 \leq i \leq n,$ are positive real numbers, according as $G$ is as in (i) or (ii).

Let $\mathsf T:=(T_1, \ldots ,T_{n-1})$ be a $G$-homogeneous $(n-1)$-tuple of rank $1$ Cowen-Douglas class, where $G$ is the the direct product of $n-1$-copies of the bi-holomorphic automorphism group of the disc. Let $\hat{T}$ be an irreducible homogeneous (with respect to the bi-holomorphic group of automorphisms of the disc) operator in the Cowen-Douglas class on the disc of rank $2$. We show that every irreducible $G$-homogeneous operator, $G$ as in (i), of rank $2$ must be of the form $(T_1\otimes I_{\widehat{H}},\ldots , T_{n-1}\otimes I_{\widehat{H}}, I_H \otimes \hat{T}).$

We also show that if $G$ is chosen to be the group as in (ii), then there are no irreducible $G$-homogeneous operators of rank $2$.

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Title: Homological Invariants and Combinatorics of Finite Simple Graphs
Speaker: Arindam Banerjee (Purdue University, USA)
Date: 15 June 2017

In this talk the interplay between the combinatorial structures of finite simple graphs and various homological invariants like regularity, depth etc. of related algebraic objects shall be discussed. Some open problems, recent developments and ongoing projects shall be discussed. In particular some new techniques developed in my thesis to study Castelnuovo-Mumford regularity of algebraic objects related to graphs shall be discussed in some details.

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Title: Boundary values, resonances and scattering poles on symmetric spaces of rank one
Speaker: Aprameyan Parthasarathy (University of Paderborn, Germany)
Date: 14 June 2017
Time: 4 pm
Venue: LH-1, Mathematics Department

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Title: Random structures: Phase transitions, scaling limits, and universality
Speaker: Sanchayan Sen (McGill University, Canada)
Date: 08 June 2017
Time: 3 pm
Venue: LH-1, Mathematics Department

The aim of this talk is to give an overview of some recent results in two interconnected areas:

a) Random discrete structures: One major conjecture in probabilistic combinatorics, formulated by statistical physicists using non-rigorous arguments and enormous simulations in the early 2000s, is as follows: for a wide array of random graph models on $n$ vertices and degree exponent $\tau>3$, typical distance both within maximal components in the critical regime as well as on the minimal spanning tree on the giant component in the supercritical regime scale like $n^{\frac{\tau\wedge 4 -3}{\tau\wedge 4 -1}}$. In other words, the degree exponent determines the universality class the random graph belongs to. The mathematical machinery available at the time was insufficient for providing a rigorous justification of this conjecture.

More generally, recent research has provided strong evidence to believe that several objects, including (i) components under critical percolation, (ii) the vacant set left by a random walk, and (iii) the minimal spanning tree, constructed on a wide class of random discrete structures converge, when viewed as metric measure spaces, to some random fractals in the Gromov-Hausdorff sense, and these limiting objects are universal under some general assumptions. We will discuss recent developments in a larger program aimed at a complete resolution of these conjectures.

b) Stochastic geometry: In contrast, less precise results are known in the case of spatial systems. We discuss a recent result concerning the length of spatial minimal spanning trees that answers a question raised by Kesten and Lee in the 90’s, the proof of which relies on a variation of Stein’s method and a quantification of a classical argument in percolation theory.

Based on joint work with Louigi Addario-Berry, Shankar Bhamidi, Nicolas Broutin, Sourav Chatterjee, Remco van der Hofstad, and Xuan Wang.

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Title: A noncommutative Matlis-Greenlees-May equivalence
Speaker: Rishi Vyas (Ben Gurion University, Israel)
Date: 06 June 2017
Time: 3 pm
Venue: LH-1, Mathematics Department

The notion of a weakly proregular sequence in a commutative ring was first formally introduced by Alonso-Jeremias-Lipman (though the property that it formalizes was already known to Grothendieck), and further studied by Schenzel and Porta-Shaul-Yekutieli: a precise definition of this notion will be given during the talk. An ideal in a commutative ring is called weakly proregular if it has a weakly proregular generating set. Every ideal in a commutative noetherian ring is weakly proregular. It turns out that weak proregularity is the appropriate context for the Matlis-Greenlees-May (MGM) equivalence: given a weakly proregular ideal I in a commutative ring A, there is an equivalence of triangulated categories (given in one direction by derived local cohomology and in the other by derived completion at I) between cohomologically I-torsion (i.e. complexes with I-torsion cohomology) and cohomologically I-complete complexes in the derived category of A.

In this talk, we will give a categorical characterization of weak proregularity: this characterization then serves as the foundation for a noncommutative generalisation of this notion. As a consequence, we will arrive at a noncommutative variant of the MGM equivalence. This work is joint with Amnon Yekutieli.

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Title: Dualizing Complexes in the Noncommutative Arithmetic Context
Speaker: Rishi Vyas (Ben Gurion University, Israel)
Date: 06 June 2017
Time: 3 pm
Venue: LH-1, Mathematics Department

Dualizing complexes were first introduced in commutative algebra and algebraic geometry by Grothendieck and play a fundamental role in Serre-Grothendieck duality theory for schemes. The notion of a dualizing complex was extended to noncommutative ring theory by Yekutieli. There are existence theorems for dualizing complexes in the noncommutative context, due to Van den Bergh, Wu, Zhang, and Yekutieli amongst others.

Most considerations of dualizing complexes over noncommutative rings are for algebras defined over fields. There are technical difficulties involved in extending this theory to algebras defined over more general commutative base rings. In this talk, we will describe these challenges and how to get around them. Time permitting, we will end by presenting an existence theorem for dualizing complexes in this more general setting.

The material described in this talk is work in progress, carried out jointly with Amnon Yekutieli.

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Title: Explaining the Earth’s surface observations: a Computational Geodynamics Approach
Speaker: Attreyee Ghosh (IISc Center for Earth Sciences)
Date: 18 May 2017
Time: 3 pm
Venue: LH-1, Mathematics Department

The field of geodynamics deals with the large scale forces shaping the Earth. Computational geodynamics, which uses numerical modeling, is one of the most important tools to understand the mechanisms within the deep Earth. With the help of these numerical models we can address some of the outstanding questions regarding the processes operating within the Earth’s interior and their control on shaping the surface of the planet. Much of Earth’s surface observations such as gravity anomalies, plate motions, dynamic topography, lithosphere stress field, owe their origin to convection within the Earth’s mantle. While we understand the basic nature of such flow in the mantle, a lot remains unexplained, including the complex rheology of the deep mantle and how this density driven convective flow couples with the shallow surface. In this talk I will discuss how my group is using numerical modeling to understand the influence of the deep mantle on surface observations.

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Title: Davenport constant and an external problem related to it
Speaker: Eshita Mazumdar (IIT, Bombay)
Date: 09 May 2017
Time: 3 pm
Venue: LH-1, Mathematics Department

For a finite abelian group $G$ with $|G| = n$, the Davenport Constant $DA(G)$ is defined to be the least integer $k$ such that any sequence $S$ with length $k$ of elements in $G$ has a non-empty $A$ weighted zero-sum subsequence. For certain sets $A$, we already know the precise value of constant corresponding to the cyclic group $\mathbb{Z} / n \mathbb{Z}$. But for different group $G$ and $A$, the precise value of it is still an open question. We try to find out bounds for these combinatorial invariant for random set $A$. We got few results in this connection. In this talk I would like to present those results and discuss about an extremal problem related to this combinatorial invariant.

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Title: Weighted norm inequalities for rough singular integral operators
Speaker: Luz Roncal (BCAM - Basque Center for Applied Mathematics, Spain)
Date: 24 April 2017
Time: 4 pm
Venue: LH-1, Mathematics Department

The study of weighted inequalities in Classical Harmonic Analysis started in 70’s, when B. Muckenhoupt characterised in 1972 the weights $w$ for which the Hardy–Littlewood maximal function is bounded in $L^p(w)$. At that time the question about how the operator depended on the constant associated with $w$, which we denote by $[w]_{A_p}$, was not considered (i.e., quantitative estimates) were not investigated.

From the beginning of 2000’s, a great activity has been carried out in order to obtain the sharp dependence for singular integral operators, reaching the solution of the so-called $A_2$ conjecture by T. P. H\“ytonen.

In this talk we consider operators with homogeneous singular kernels, on which we assume smoothness conditions that are weaker than the standard ones (this is why they are called rough). The first qualitative weighted estimates are due to J. Duoandikoetxea and J. L. Rubio de Francia. For the norm of these operators in the space $L^2(w)$ we obtain a quantitative estimate which is quadratic in the constant $[w]_{A_2}$.

The results are based on a classical decomposition of the rough operators as a sum of other operators with a smoother kernel, for which a quantitative reelaboration of a dyadic decomposition proposed by M. T. Lacey is applied.

We will overview as well the most recent advances, mainly associated with quantitative estimates for these rough singular integrals. In particular, Coifman-Fefferman type inequalities (which are new even in their qualitative version), weighted $A_p$-$A_{\infty}$ inequalities and a quantitative version of weak $(1,1)$ estimates will be shown.

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Title: Conformal blocks, strange duality and the moduli space of curves
Speaker: Swarnava Mukhopadhyay (University of Maryland, USA)
Date: 21 April 2017
Time: 10 am
Venue: LH-1, Mathematics Department (via Skype)

Conformal blocks are refined invariants of tensor product of representations of a Lie algebra that give a special class of vector bundles on the moduli space of curves. In this talk, I will introduce conformal blocks and explore connections to questions in algebraic geometry and representation theory. I will also focus on some ``strange” dualities in representation theory and how they give equalities of divisor classes on the moduli space of curves.

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Title: Riemann-Roch, Alexander Duality and Free Resolutions
Speaker: Madhusudan Manjunath (Mathematisches Forschungsinstitut Oberwolfach, Germany)
Date: 20 April 2017
Time: 4 pm
Venue: LH-1, Mathematics Department (via Skype)

The Riemann-Roch theorem is fundamental to algebraic geometry. In 2006, Baker and Norine discovered an analogue of the Riemann-Roch theorem for graphs. In fact, this theorem is not a mere analogue but has concrete relations with its algebro-geometric counterpart. Since its conception this topic has been explored in different directions, two significant directions are i. Connections to topics in discrete geometry and commutative algebra ii. As a tool to studying linear series on algebraic curves. We will provide a glimpse of these developments. Topics in commutative algebra such as Alexander duality and minimal free resolutions will make an appearance. This talk is based on my dissertation and joint work with i. Bernd Sturmfels, ii. Frank-Olaf Schreyer and John Wilmes and iii. an ongoing work with Alex Fink.

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Title: A quantitative form of Schoenberg's theorem in fixed dimension
Speaker: Alexander Belton (Lancaster University, UK)
Date: 05 April 2017
Time: 4 pm
Venue: LH-1, Mathematics Department

The Hadamard product of two matrices is formed by multiplying corresponding entries, and the Schur product theorem states that this operation preserves positive semidefiniteness.

It follows immediately that every analytic function with non-negative Maclaurin coefficients, when applied entrywise, preserves positive semidefiniteness for matrices of any order. The converse is due to Schoenberg: a function which preserves positive semidefiniteness for matrices of arbitrary order is necessarily analytic and has non-negative Maclaurin coefficients.

For matrices of fixed order, the situation is more interesting. This talk will present recent work which shows the existence of polynomials with negative leading term which preserve positive semidefiniteness, and characterises precisely how large this term may be. (Joint work with D. Guillot, A. Khare and M. Putinar.)

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Title: On commutators of singular integral operators with BMO functions
Speaker: Carlos Perez (University of Basque Country)
Date: 28 March 2017
Time: 4 pm
Venue: LH-1, Mathematics Department

Commutators of singular integral operators with BMO functions were introduced in the seventies by Coifman-Rochberg and Weiss. These operators are very interesting for many reasons, one of them being the fact that they are more singular than Calderon-Zygmund operators. In this lecture we plan to give several reasons showing the “bad” behavior of these operators.

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Title: Detecting free splittings
Speaker: Suraj Kumar (Paris Diderot University, France)
Date: 14 March 2017
Time: 9:30 am
Venue: LH-1, Mathematics Department

The goal of this talk is to present an algorithm which takes a compact square complex belonging to a special class as input and decides whether its fundamental group splits as a free product. The special class is built by attaching tubes to finite graphs in such a way that they satisfy a nonpositive curvature condition. This construction gives rise to a rich class of complexes, including, but not limited to, closed surfaces of positive genus. The algorithm can be used to deduce the celebrated Stallings theorem for this special class, as also the well known Grushko decomposition theorem.

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Title: When is R[\theta] integrally closed?
Speaker: Sudesh K Khanduja (IISER Mohali)
Date: 10 March 2017
Time: 4 pm
Venue: LH-1, Mathematics Department

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Title: A result for boolean interval of finite groups
Speaker: Mamta Balodi (IMSc)
Date: 09 March 2017
Time: 4 pm
Venue: LH-3, Mathematics Department

A group is cyclic iff its subgroup lattice is distributive. Ore’s generalized one direction of this result. We will discuss a dual version of Ore’s result, for any boolean interval of finite groups under the assumption that the dual Euler totient of the interval is nonzero. We conjecture that the dual Euler totient is always nonzero for boolean intervals. We will discuss some techniques which may be helpful in proving it. We first see that dual Euler totient of an interval of finite groups is the Mobius invariant (upto a sign) of its coset poset P. Next in the boolean group complemented case, we prove that P is Cohen-Macaulay, using the existence of an explicit EL-labeling. We then see that nontrivial betti number of the order complex is nonzero, and so is the dual Euler totient.

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Title: Diamond lemma for group graded quasi-algebras
Speaker: Mamta Balodi (IMSc)
Date: 02 March 2017
Time: 4 pm
Venue: LH-1, Mathematics Department

Quasi-algebras were introduced as algebras in a monoidal category. Since the associativity constraints in these categories are allowed to be nontrivial, the class of quasi-algebras contains various important examples of non-associative algebras like the octonions and other Cayley algebras. The diamond lemma is a reduction method used in algebra. The original diamond lemma was stated in graph theory by Newman which was later generalized to associative algebras by Bergman. In this talk, we will see the analog of this lemma for the group graded quasi-algebras with some interesting examples like octonion algebra and generalized octonions

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Title: Theoretical models for compressible vortex streets
Speaker: Vikas Krishnamurthy (Imperial College, London)
Date: 23 February 2017
Time: 4 pm
Venue: LH-3, Mathematics Department

Vortex streets are a common feature of fluid flows at high Reynolds numbers and their study is now well developed for incompressible fluids. Much less is known, however, about compressible vortex streets. A fundamental reason appears to be the inapplicability of the point vortex model to compressible flows. In this talk, we discuss point vortices in the context of weakly compressible flows and elaborate on the problems involved. We then adopt the hollow vortex model where each vortex is modelled as a finite-area constant pressure region with non-zero circulation. For weakly compressible flows steady hollow vortex solutions are well known to be candidates for the leading order solution in a perturbative Rayleigh-Jansen expansion of a compressible flow. Here we give details of that expansion based on the vortex street solutions of Crowdy & Green (2012). Physical properties of the compressible vortex streets are described. Our approach uses the Imai-Lamla method coupled with analytic function theory and conformal mapping. (Joint work with Darren Crowdy)

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Title: Punctual gluing of t-structures in algebraic geometry
Speaker: Vaibhav Vaish (ISI Bangalore)
Date: 17 February 2017
Time: 2:15 pm
Venue: LH-1, Mathematics Department

The formalism of an “abelian category’’ is meant to axiomatize the operations of linear algebra. From there, the notion of “derived category’’ as the category of complexes “upto quasi-isomorphisms’’ is natural, motivated in part by topology. The formalism of t-structures allows one to construct new abelian categories which are quite useful in practice (giving rise to new cohomology theories like intersection cohomology, for example). In this talk we want to discuss a notion of punctual (=”point-wise’’) gluing of t-structures which is possible in the context of algebraic geometry. The essence of the construction is classical and well known, but the new language leads to useful constructions in the motivic world.

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Title: Flow Invariance Preserving Feedback Controllers for Sabra Shell Model of Turbulence
Speaker: Dharmatti Sheetal (IISER TVM)
Date: 17 February 2017
Time: 11 am
Venue: LH-1, Mathematics Department

In this talk, I would continue dealing with Sabra shell model of Turbulence and study one of the important questions for fluid flow problems namely, finding controls which are capable of preserving the invariant quantities of the flow. Controls are designed in the feedback form such that resultant controlled flow will preserve certain physical properties of the state such as enstrophy, helicity. We use the theory of nonlinear semigroups and represent the feedback control as a multi-valued feedback term which lies in the normal cone of the convex constraint space under consideration.

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Title: Graph Partitioning using its Spectra
Speaker: Anand Louis (IISc Computer Science and Automation)
Date: 17 February 2017
Time: 3:30 pm
Venue: LH-1, Mathematics Department

Graph-partitioning problems are a central topic of research in the study of algorithms and complexity theory. They are of interest to theoreticians with connections to error correcting codes, sampling algorithms, metric embeddings, among others, and to practitioners, as algorithms for graph partitioning can be used as fundamental building blocks in many applications. One of the central problems studied in this field is the sparsest cut problem, where we want to compute the cut which has the least ratio of number of edges cut to size of smaller side of the cut. This ratio is known as the expansion of the cut. In this talk, I will talk about higher order variants of expansion (i.e. notions of expansion corresponding to partitioning the graph into more than two pieces, etc.), and how they relate to the graph’s eigenvalues. The proofs will also show how to use the graph’s eigenvectors to compute partitions satisfying these bounds. Based on joint works with Prasad Raghavendra, Prasad Tetali and Santosh Vempala.

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Title: Control and analysis of Shell model of Turbulence
Speaker: Dharmatti Sheetal (IISER TVM)
Date: 16 February 2017
Time: 3:30 pm
Venue: LH-1, Mathematics Department

In this lecture I am going to present control problems associated with shell models of Turbulence. Shell models of turbulence are simplified caricatures of equations of fluid mechanics in wave-vector representation. They exhibit anomalous scaling and local non-linear interactions in wave number space. We would like to study control problem related to one such widely accepted shell model of turbulence known as sabra shell model. We associate two cost functionals: one ensures minimizing turbulence in the system and the other addresses the need of taking the ow near a priori known state. We derive the optimal controls in terms of the solution of adjoint equation for corresponding linearised problems.

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Title: Playing with the nonlinearity of the Navier-Stokes Equation
Speaker: Samriddhi Sankar Ray (ICTS)
Date: 03 February 2017
Time: 2:15 pm
Venue: LH-1, Mathematics Department

Understanding the origins of intermittency in turbulence remains one of the most fundamental challenges in applied mathematics. In recent years there has been a fresh attempt to understand this problem through the development of the method of Fourier decimation. In this talk, we will review these recent results and analyse the role of precise numerical simulations in understanding the mathematics of the Navier-Stokes and Euler equations.

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Title: What is finiteness?
Speaker: Abhishek Banerjee (IISc Mathematics)
Date: 03 February 2017
Time: 3:30 pm
Venue: LH-1, Mathematics Department

It is generally well known that there is an innate notion of things like isomorphisms or epimorphisms. This allows us to talk about isomorphisms or epimorphisms of various objects: groups, rings, algebras,etc. In other words, “isomorphism” is really a categorical notion.However, it is not so well known that finiteness itself is alsocategorical. In this talk, we will discuss how finiteness applies tovarious categories. This will allow usto see finite sets, finite dimensional vector spaces, finitely generated algebras and compact sets as manifestations of the same basic idea.

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Title: Hole probabilities for determinantal point processes in the complex plane
Speaker: Kartick Adhikari (IISc Mathematics)
Date: 31 January 2017
Time: 11 am
Venue: LH-1, Mathematics Department

Consider the infinite Ginibre ensemble (the distributional limit of the eigenvalues of nxn random matrices with i.i.d. standard complex Gaussian entries) in the complex plane. For a bounded set U, let H_r(U) denote the probability (hole probability) that no points of infinite Ginibre ensemble fall in the region rU. We study the asymptotic behavior of H_r(U) as r–>\infty. Under certain conditions on U we show that \log H_r(U)=C_U.r^4 (1+o(1)) as r–> \infty. Using potential theory, we give an explicit formula for C_U in terms of the minimum logarithmic energy of the set with a quadratic external field. We calculate C_U explicitly for some special sets such as the annulus, cardioid, ellipse, equilateral triangle and half disk.

Moreover, we generalize the above hole probability results for a class of determinantal point processes in the complex plane.

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Title: The Space of Metric Measure Spaces
Speaker: Sayantan Maitra (IISc Mathematics)
Date: 20 January 2017
Time: 11 am
Venue: LH-1, Mathematics Department

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Title: Linking numbers for algebraic cycles
Speaker: Souvik Goswami (ICMAT, Madrid, Spain)
Date: 18 January 2017
Time: 4 pm
Venue: LH-1, Mathematics Department

In algebraic geometry the concept of height pairing (a particular example of linking numbers) of algebraic cycles lies at the confluence of arithmetic, Hodge theory and topology. In a series of two talks, I will explain the notion of Beilinson’s height pairing for cycles homologous to zero. This will bring into picture the notion of Arakelov/arithmetic intersection theory. I will give sufficient background of this theory and provide examples. Finally, I will talk about my recent work with Dr. Jose Ignacio Burgos, about a generalization of Beilinson’s height pairing for higher algebraic cycles.

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Title: Approximate controllability of an impulsive sub-diffusion equation
Speaker: Lakshman Mahato (IIIT Dharwad)
Date: 13 January 2017

In this talk, I shall consider an abstract Cauchy problem for a class of impulsive sub-diffusion equation. Existence and regularity of solution of the problem shall be established via eigenfunction expansion. Further, I shall establish the approximate controllability of the problem by applying unique continuation property via internal control acts on a sub-domain.

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Title: Limiting measure for TASEP with a slow bond
Speaker: Sourav Sarkar (UC Berkeley, USA)
Date: 11 January 2017
Time: 3 pm
Venue: LH-1, Mathematics Department

It was shown by Basu, Sidoravicius and Sly that a TASEP starting with the step initial condition, i.e., with one particle each at every nonpositive site of $\mathbb{Z}$ and no particle at positive sites, with a slow bond at the origin where a particle jumping from the origin jumps at a smaller rate $r < 1$, has an asympototic current which is strictly less than 1/4. Here we study the limiting measure of the TASEP with a slow bond. The distribution of regular TASEP started with the step initial condition converges to the invariant product Bernoulli measure with density 1/2. The slowdown due to the slow bond implies that there is a long range effect near the origin where the region to the right of origin is sparser and there is a traffic jam to the left of the slow bond with particle density higher than a half. However, the distribution becomes close to a product Bernoulli measure as one moves far away from the origin, albeit with a different density ? < 1/2 to the right of the origin and ?’ > 1/2 to the left of the origin. This answers a question due to Liggett. The proof uses the correspondence between TASEP and directed last passage percolation on $\mathbb{Z}^2$ with exponential passage times, and the geometric properties of the maximal paths there.

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Title: Upscaling of a System of Semilinear Diffusion Reaction Equations in a Heterogeneous Medium: MultiScale Modeling and Periodic Homogenization
Speaker: Hari Shankar Mahato (University of Georgia, USA)
Date: 10 January 2017
Time: 11 am
Venue: LH-1, Mathematics Department

A porous medium (concrete, soil, rocks, water reservoir, e.g.) is a multiscale medium where the heterogeneities present in the medium are characterized by the micro scale and the global behaviors of the medium are observed at the macro scale. The upscaling from the micro scale to the macro scale can be done via averaging methods.

In this talk, diffusion and reaction of several mobile chemical species are considered in the pore space of a heterogeneous porous medium. The reactions amongst the species are modelled via mass action kinetics and the modelling leads to a system of multispecies diffusion; reaction equations (coupled semi-linear partial differential equations) at the micro scale where the highly nonlinear reaction rate terms are present at the right hand sides of the system of PDEs, cf. [2]. The existence of a unique positive global weak solution is shown with the help of a Lyapunov functional, Schaefer’s fixed point theorem and maximal Lp-regularity, cf. [2, 3]. Finally, with the help of periodic homogenization and two-scale convergence we upscale the model from the micro scale to the macro scale, e.g. [1, 3]. Some numerical simulations will also be shown in this talk, however for the purpose of illustration, we restrict ourselves to some relatively simple 2- dimensional situations.

As an extension to the previous model, we consider the mixture of two fluids. For such models, a system of Stokes-Cahn-Hilliard equations will be considered at the micro scale in a perforated porous medium. We first explain the periodic setting of the model and the existence results. At the end homogenization of the model will be shown using some extension theorems on Sobolev spaces, two-scale convergence and periodic unfolding.

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Title: Finite point configurations
Speaker: Eyvindur A. Palsson (Virginia Tech, USA)
Date: 09 January 2017
Time: 4 pm
Venue: LH-1, Mathematics Department

As big data sets have become more common, there has been significant interest in finding and understanding patterns in them. One example of a simple pattern is the distance between data points, which can be thought of as a 2-point configuration. Two classic questions, the Erdos distinct distance problem, which asks about the least number of distinct distances determined by N points in the plane, and its continuous analog, the Falconer distance problem, explore that simple pattern. Questions similar to the Erdos distinct distance problem and the Falconer distance problem can also be posed for more complicated patterns such as triangles, which can be viewed as 3-point configurations. In this talk I will present recent Falconer type theorems, established by myself and my collaborators, for a wide class of finite point configurations in any dimension. The techniques we used come from analysis and geometric measure theory, and the key step was to obtain bounds on multilinear analogues of generalized Radon transforms.

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Title: Siegel-Veech transforms are in L2
Speaker: Jayadev Athreya (University of Washington, USA)
Date: 06 January 2017
Time: 11 am
Venue: LH-1, Mathematics Department

Let H denote a connected component of a stratum of translation surfaces. We show that the Siegel-Veech transform of a bounded compactly supported function on R2 is in L2(H,μ), where μ is the Masur-Veech measure on H, and give applications to bounding error terms for counting problems for saddle connections. We will review classical results in the Geometry of Numbers which anticipate this result. This is joint work with Yitwah Cheung and Howard Masur.

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Title: On some fourth order equations associated to Physics
Speaker: Sanjiban Santra (CIMAT, Mexico)
Date: 05 January 2017
Time: 4 pm
Venue: LH-1, Mathematics Department

We consider a fourth order traveling wave equation associated to the Suspension Bridge Problem (SBP). This equations are modeled by the traveling wave behavior on the Narrows Tacoma and the Golden Gate bridge. We prove existence of homoclinic solutions when the wave speed is small. We will also discuss the associated fourth order Liouville theorem to the problem and possible link with the De Giorgi’s conjecture. This is an attempt to prove the McKenna-Walter conjecture which is open for the last two decades.

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Title: A glimpse at bi-free probability.
Speaker: Dan-Virgil Voiculescu (University of California, Berkeley, USA)
Date: 28 December 2016
Time: 3.30pm
Venue: LH-1

I will provide a glimpse at the recent extension of free probability to systems with left and right variables based on a notion of bi-freeness. This will include the simplest cases of nonlinear convolution operations on non-commutative distributions snd the analogue of extreme values in this setting.

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Title: Homological Algebra of Ideals Related to Finite Simple Graphs.
Speaker: Arindam Banerjee (Purdue University, USA)
Date: 27 December 2016
Time: 3 pm
Venue: LH-1

Given any finite simple graph G one can naturally associate two ideals, namely the edge ideal I(G) and the binomial edge ideal J_G in suitable polynomial rings. In this talk we shall discuss the interplay between combinatorics of the graph and depth and regularity of I(G), J_G and their powers. Some recent progress and some open problems will be discussed.

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Title: On 3+1 Lorentzian Einstein manifolds with one rotational isometry.
Speaker: Dr. Nishanth Gudapati Affiliation: Yale University, USA
Date: 21 December 2016
Time: 11:00 am.
Venue: LH-1, Department of Mathematics, IISc.

Differentiable manifolds whose Ricci curvature is proportional to the metric are called Einstein manifolds. Such manifolds have been central objects of study in differential geometry and Einstein’s theory for general relativity, with some strong recent results. In this talk, we shall focus on positively curved 3+1 Lorentzian Einstein manifolds with one spacelike rotational isometry. After performing the dimensional reduction to a 2+1 dimensional Einstein’s equations coupled to ‘shifted’ wave maps, we shall prove two explicit positive mass theorems:

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Title: Coarse Geometry for Noncommutative Spaces
Speaker: Tathagata Banerjee
Date: 19 December 2016
Time: 3pm
Venue: LH-1

Abstract: Given a proper coarse structure on a locally compact Hausdorff space $X$, one can construct the Higson compactification for the coarse structure. In the opposite direction given a compactification of $X$, one can construct a coarse structure. We use unitizations of a non-unital C$^*$\\nobreakdash- algebra $A$ to define a noncommutative coarse structure on $A$. We also set up a framework to abstract coarse maps to this noncommutative setting. The original motivation for this work comes from Physics where quantum phenomenon when probed at large scales give classical results. We show equivalence of the canonical coarse structure on the classical plane $\\mathbb{R}^{2n}$ with a certain noncommutative coarse structure on the Moyal plane which models the hypothetical phase space of Quantum physics. If time permits we shall also discuss other examples of noncommutative coarse equivalences. This is a joint work with Prof. Ralf Meyer.

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Title: Adaptive wavelet-based methods for solution of PDEs and signal analysis.
Speaker: Ratikant Behra (IISER-Kolkata)
Date: 09 December 2016
Time: 3 pm
Venue: LH-1

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Title: Entrywise functions preserving positivity: Connections between analysis, algebra, and combinatorics
Speaker: Apoorva Khare (Stanford University, USA)
Date: 08 December 2016
Time: 11 am
Venue: LH-1 (via Skype)

What functions preserve positive semidefiniteness (psd) when applied entrywise to psd matrices? This question has a long history beginning with Schur, Schoenberg, and Rudin, and has also recently received renewed attention due to its applications in high-dimensional statistics. However, effective characterizations of entrywise functions preserving positivity in a fixed dimension remain elusive to date.

I will present recent progress on this question, obtained by: (a) imposing rank and sparsity constraints, (b) restricting to structured matrices, and (c) restricting the class of functions to special families such as polynomials or power functions. These constraints arise in theory as well as applications, and provide natural ways to relax the elusive original problem. Moreover, novel connections to symmetric function theory, matrix analysis, and combinatorics emerge out of these refinements.

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Title: Some Recent Progress in Quasilinear Hyperbolic Systems: New Local Solvability Methods and Stochastic Analysis.
Speaker: Manil Mohan (Air Force Institute of Tech, Ohio)
Date: 06 December 2016
Time: 11 am
Venue: LH-1

Quasilinear symmetric and symmetrizable hyperbolic system has a wide range of applications in engineering and physics including unsteady Euler and potential equations of gas dynamics, inviscid magnetohydrodynamic (MHD) equations, shallow water equations, non-Newtonian fluid dynamics, and Einstein field equations of general relativity. In the past, the Cauchy problem of smooth solutions for these systems has been studied by several mathematicians using semigroup approach and fixed point arguments. In a recent work of M. T. Mohan and S. S. Sritharan, the local solvability of symmetric hyperbolic system is established using two different methods, viz. local monotonicity method and a frequency truncation method. The local existence and uniqueness of solutions of symmetrizable hyperbolic system is also proved by them using a frequency truncation method. Later they established the local solvability of the stochastic quasilinear symmetric hyperbolic system perturbed by Levy noise using a stochastic generalization of the localized Minty-Browder technique. Under a smallness assumption on the initial data, a global solvability for the multiplicative noise case is also proved. The essence of this talk is to give an overview of these new local solvability methods and their applications.

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Title: The Narasimhan Seshadri Theorem revisited
Speaker: M S Raghunathan
Date: 02 December 2016
Time: 3 pm
Venue: LH-1

We give a relatively simple proof of the famous theorem of Narasimhan and Seshadri on vector bundles on a compact Riemann surface. The theorem relates the algebraic geometric notion of stability of vector bundles on a compact Riemann surface with a transcendental construct - unitary representations of a suitable Fuchsian group associated to the Riemann surface.

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Title: The Narasimhan Seshadri Theorem revisited
Speaker: M S Raghunathan (National Center for Mathematics, IIT Mumbai)
Date: 02 December 2016
Time: 3 pm
Venue: LH-1

We give a relatively simple proof of the famous theorem of Narasimhan and Seshadri on vector bundles on a compact Riemann surface. The theorem relates the algebraic geometric notion of stability of vector bundles on a compact Riemann surface with a transcendental construct - unitary representations of a suitable Fuchsian group associated to the Riemann surface.

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Title: Torelli theorem for the parabolic Deligne-Hitchin moduli space
Speaker: Tomas Gomez (ICMAT, Spain)
Date: 14 November 2016
Time: 3pm
Venue: LH-1

The Deligne-Hitchin moduli space is a partial compactification of the moduli space of $\lambda$-connections. It includes as closed subvarieties the moduli spaces of Hitchin bundles ($\lambda=0$) and of holomorphic connections ($\lambda=1$), exhibiting the later as a deformation of the former. We show a Torelli theorem for a parabolic version of this moduli space (joint work with David Alfaya). I will try to make the talk accessible to a wide mathematical audience.

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Title: The Perron-Frobenius theorem and its application to a class of dynamical systems
Speaker: Sandeep Krishna, NCBS.
Date: 28 October 2016
Venue: Simons Centre, Ground Floor.

The Perron-Frobenius theorem is a powerful and useful result about the eigenvalues and eigenvectors of a non-negative matrix. I will not be proving the theorem but will instead focus on its applications. In particular, I will discuss how it can be used to understand the behaviour of a certain class of dynamical systems, namely certain systems of first-order ordinary differential equations where the couplings between variables are specified by a graph. Some familiarity with graph theory will be useful, but I will try to recapitulate all the basic concepts needed for this talk.

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Title: Simultaneous Similarity Classes of tuples of Commuting matrices.
Speaker: Uday Bhaskar (IMSc, Chennai)
Date: 07 October 2016
Time: 2 pm
Venue: LH-1

The enumeration of isomorphism classes of modules of a polynomial algebra in several variables over a finite field is the same as the classifi cation of commuting tuples of matrices over a finite field up to simultaneous similarity. Let C_{n,k}(q) denote the number of isomorphism classes of n-dimensional Fq[x1,…,xk]-modules. The generating function in k of the C_{n,k}(q) is a rational function. The computation of this was done explicitly for n <= 4. I shall give a summary of my recently published work on this study of the C_{n,k}(q)s for n <= 2.

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Title: Domains of holomorphy for irreducible admissible Banach representations
Speaker: Dr Aprameyan Parthasarathy( Universitat Padernorn, Germany)
Date: 27 September 2016
Time: 4pm
Venue: LH-1

In this talk, we’ll report on progress towards a conjecture of B.Krtz about the holomorphic extensions of non-zero K-finite vectors of irreducible admissible Banach representations of simple real Lie groups and the relation to a distinguished domain - the so-called crown domain. We’ll explain some of the main ideas - the Casselman-Wallach smooth globalisation, vanishing of matrix coefficients at infinity etc. Indeed we prove the conjecture with some additional growth conditions on the Banach globalisations. This is joint work with Gang Liu, Uni. Metz.

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Title: Epimorphically Preserved Semigroup Identities
Speaker: Wajih Ashraf
Date: 23 September 2016
Time: 4 pm
Venue: LH-1

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Title: Margulis spacetimes and Anosov representations
Speaker: Sourav Ghosh (Universitat Heidelberg, Germany)
Date: 20 September 2016
Time: 4 pm
Venue: LH-1

In this talk I will describe the interrelationship between Margulis spacetimes and Anosov representations. Moreover, I will define the pressure metric on the moduli space of Margulis spacetimes and sketch some of it’s properties.

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Title: Tropical Algebraic Geometry: an Introduction.
Speaker: Madhusudan Manjunath (Queen Mary Univ of London, UK)
Date: 06 September 2016
Time: 4 pm
Venue: LH-1

We start with a gentle introduction to tropical algebraic geometry. We then focus on the tropical lifting problem and discuss recent progress. Tropical analogues of graph curves play an important role in this study. This talk will be accessible to the general mathematical audience.

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Title: Tropical Algebraic Geometry: an Introduction.
Speaker: Madhusudan Manjunath (Queen Mary Univ of London, UK)
Date: 05 September 2016
Time: 4 pm
Venue: LH-1

We start with a gentle introduction to tropical algebraic geometry. We then focus on the tropical lifting problem and discuss recent progress. Tropical analogues of graph curves play an important role in this study. This talk will be accessible to the general mathematical audience.

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Title: Multiobjective optimisation and tropical geometry
Speaker: Prof Benjamin Burton, (The University of Queensland, Australia)
Date: 02 September 2016
Venue: LH-1

Multiobjective optimisation involves optimising several quantities, such as time and money, simultaneously. The result is a polyhedral frontier of best possible solutions, which cannot improve one quantity without a trade-off against another. For linear programming, this frontier can be generated using Benson’s outer approximation algorithm, which uses a sequence of scalarisations (single-objective optimisations), combined with classical algorithms from polytope theory.

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Title: A hybrid HPC framework with analysis for a class of stochastic models
Speaker: M. Ganesh, Professor, Colorado School of Mines
Date: 19 August 2016
Venue: LH-1

We consider a class of wave propagation models with aleatoric and epistemic uncertainties. Using mathematical analysis-based, shape-independent, a priori parameter estimates, we develop offline/online strategies to compute statistical moments of a key quantity of interest in such models. We present an efficient reduced order model (ROM) and high performance computing (HPC) framework with analysis for quantifying aleatoric and epistemic uncertainties in the propagation of waves through a stochastic media comprising a large number of three dimensional particles. Simulation even for a single deterministic three dimensional configuration is inherently difficult because of the large number of particles. The aleatoric uncertainty in the model leads to a larger dimensional system involving three spatial variables and additional stochastic variables. Accounting for epistemic uncertainty in key parameters of the input probability distributions leads to prohibitive computational complexity. Our hybrid ROM and HPC framework can be used in conjunction with any computational method to simulate a single particle deterministic wave propagation model.

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Title: On residues of certain intertwining operators
Speaker: Sandeep Varma (TIFR, Mumbai)
Date: 16 August 2016
Venue: LH-I, Department of Mathematics

Let $G$ be a connected reductive group over a finite extension $F$ of $\mathbb{Q}_p$. Let $P = MN$ be a Levi decomposition of a maximal parabolic subgroup of $G$, and $\sigma$ an irreducible unitary supercuspidal representation of $M(F)$. One can then consider the representation Ind$_{P(F)}^{G(F)}\sigma$ (normalized parabolic induction). This induced representation is known to be either irreducible or of length two. The question of when it is irreducible turns out to be (conjecturally) related to local $L$-functions, and also to poles of a family of so called intertwining operators.

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Title: Resonances for the Laplacian on Riemannian symmetric spaces of the noncompact type: the rank two case
Speaker: Angela Pasquale
Date: 04 August 2016
Time: 4 pm
Venue: LH-1

Let $\Delta$ be the Laplacian on a Riemannian symmetric space $X=G/K$ of the noncompact type and let $\sigma(\Delta)\subseteq \mathbb{C}$ denote its spectrum. The resolvent $(\Delta-z)^{-1}$ is a holomorphic function on $\mathbb{C} \setminus \sigma(\Delta)$, with values in the space of bounded operators on $L^2(X)$. If we view it as a function with values in Hom$(C_c^\infty(X), C_c^\infty(X)^*)$, then it often admits a meromorphic continuation beyond $\mathbb{C} \setminus \sigma(\Delta)$. We study this meromorphic continuation as a map defined on a Riemann surface above $\mathbb{C} \setminus \sigma(\Delta)$. The poles of the meromorphically extended resolvent are called resonances. The image of the residue operator at a resonance is a $G$-module. The main problems are the existence and the localization of the resonances as well as the study of the (spherical) representations of $G$ so obtained. In this talk, based on joint works with Joachim Hilgert and Tomasz Przebinda, we will describe a variety of different situations occurring in the rank two case.

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Title: Geometry of Geodesics in Random Spatial Processes : Exactly Solvable Models and Beyond
Speaker: Prof. Riddhipratim Basu (Stanford university)
Date: 28 July 2016
Time: 4.00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Kardar, Parisi and Zhang introduced a universality class (the so-called KPZ universality class) in 1986 which is believed to explain the universal behaviour in a large class of two dimensional random growth models including first and last passage percolation. A number of breakthroughs has led to an explosion of mathematically rigorous results in this field in recent years. However, these have mostly been restricted to the class of exactly solvable models, where exact formulae are available using powerful tools of random matrices, algebraic combinatorics and representation theory; beyond this class the understanding remains rather limited. I shall talk about a geometric approach to these problems based on studying the geometry of geodesics (optimal paths), and describe some recent progress along these lines.

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Title: Representation homology
Speaker: Ajay Ramadoss, Indiana University
Date: 27 July 2016
Time: 11:15 am
Venue: LH-1, Department of Mathematics

The n-dimensional matrix representations of a group or an associative algebra A form a space (algebraic variety) Rep(A,n) called the n-th representation variety of A. This is a classical geometric invariant that plays a role in many areas of mathematics. The construction of Rep(A,n) is natural (functorial) in A, but it is not `exact’ in the sense of homological algebra. In this talk, we will explain how to refine Rep(A,n) by constructing a derived representation variety DRep(A,n), which is an example of a derived moduli space in algebraic geometry. For an application, we will look at the classical varieties of commuting matrices, and present a series of combinatorial conjectures extending the famous Macdonald conjectures in representation theory.

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Title: Representation homology
Speaker: Ajay Ramadoss, Indiana University
Date: 26 July 2016
Time: 11:00 a.m.
Venue: LH-1, Department of Mathematics

The n-dimensional matrix representations of a group or an associative algebra A form a space (algebraic variety) Rep(A,n) called the n-th representation variety of A. This is a classical geometric invariant that plays a role in many areas of mathematics. The construction of Rep(A,n) is natural (functorial) in A, but it is not `exact’ in the sense of homological algebra. In this talk, we will explain how to refine Rep(A,n) by constructing a derived representation variety DRep(A,n), which is an example of a derived moduli space in algebraic geometry. For an application, we will look at the classical varieties of commuting matrices, and present a series of combinatorial conjectures extending the famous Macdonald conjectures in representation theory.

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Title: Rank-level duality of Conformal Blocks
Speaker: Swarnava Mukhopadhyay University of Maryland
Date: 25 July 2016
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

Classical invariants for representations of one Lie group can often be related to invariants of some other Lie group. Physics suggests that the right objects to consider for these questions are certain refinements of classical invariants known as conformal blocks. Conformal blocks appear in algebraic geometry as spaces of global sections of line bundles on the moduli stack of parabolic bundles on a smooth curve. Rank-level duality connects a conformal block associated to one Lie algebra to a conformal block for a different Lie algebra.

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Title: Rank-level duality of Conformal Blocks
Speaker: Swarnava Mukhopadhyay (Univ of Maryland, College Park)
Date: 25 July 2016
Time: 3:30 pm
Venue: LH-1

Classical invariants for representations of one Lie group can often be related to invariants of some other Lie group. Physics suggests that the right objects to consider for these questions are certain refinements of classical invariants known as conformal blocks. Conformal blocks appear in algebraic geometry as spaces of global sections of line bundles on the moduli stack of parabolic bundles on a smooth curve. Rank-level duality connects a conformal block associated to one Lie algebra to a conformal block for a different Lie algebra.

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Title: Algebraic K and L-theory of groups acting on trees
Speaker: S K Roushon (TIFR, Mumbai)
Date: 26 May 2016
Time: 3:30-4:30 pm
Venue: LH-2

The Farrell-Jones Isomorphism conjecture gives a single statement to understand many standard conjectures in Topology and Algebra= . We will discuss understanding K and L-theory of groups acting on trees from the vertex stabilizers of the action, in the context of Isomorphism conjecture.

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Title: Relation between orbit spaces of unimodular elements and improved stability bound
Speaker: Pratyusha Chattopadhyay (ISI Bengaluru)
Date: 05 May 2016
Time: 3:30 pm
Venue: LH-1

This is a topic in classical algebraic K-Theory. I will recall definitions of elementary linear group, elementary symplectic group, linear transvection group, and symplectic transvection group. These group= s have natural action on the set of unimodular elements. I will briefly discuss how bijections between orbit spaces of unimodular elements under different group actions are established. Finally, I will talk about an application of these results, namely improving injective stability bound for the K1 group.

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Title: Unique factorization of tensor products for finite-dimensional simple Lie algebras
Speaker: R. Venkatesh ( Weizmann Institute of Science, Israel)
Date: 21 April 2016
Time: 2 pm
Venue: LH-1 (via Skype)

Suppose V is a finite dimensional representation of a complex finite dimensional simple Lie algebra that can be written as a tensor product of irreducible representations. A theorem of C.S. Rajan states that the non-trivial irreducible factors that occur in the tensor product factorization of V are uniquely determined, up to reordering, by the isomorphism class of V. I will present an elementary proof of Rajan’s theorem. This is a joint work with S.Viswanath.

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Title: Boundary behaviour of the Kobayashi distance and horosphere boundary in complete hyperbolic manifolds.
Speaker: Herve Gaussier Fourier Institute, Grenoble
Date: 13 April 2016

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Title: : Optimal Control Problems and Homogenization
Speaker: Mr. Bidhan Chandra Sardar Ph. D. Research Student
Date: 06 April 2016
Time: 11.00 a.m.
Venue: Lecture Hall I,Dept of Mathematics

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Title: Chromatic polynomials of graphs from Kac-Moody algebras.
Speaker: R. Venkatesh ( Weizmann Institute of Science, Israel)
Date: 16 March 2016
Time: 2 pm
Venue: LH-1

Given a simple graph G, the Kac-Moody Lie algebra of G is the Kac-Moody algebra whose simply laced Dynkin diagram is G. We give a new interpretation of the chromatic polynomial of G in terms of the Kac-Moody Lie algebra of G. We show that the chromatic polynomial is essentially th= e q-Kostant partition function of the associated Kac-Moody algebra evaluate= d on the sum of the simple roots. As an application, we construct basis of some of the root spaces of the Kac-Moody algebra of G. This is a joint work with Sankaran Viswanath.

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Title: Exchangeable and stationary chains of quantum Gaussian states and an integral formula for their entropy rates.
Speaker: K R Parthasarathy
Date: 11 March 2016
Time: 4 pm
Venue: LH-1

We shall introduce the definition of a k-mode Gaussian state and a chain of such states which determine a C* probability space. We present examples of such states exhibiting properties like exchangeability and stationarity. Stationary chains are determined by block Toeplitz matrices. Using the Kac-Murdoch-Szego theorems on asymptotic spectral distributions of Toeplitz matrices we compute the entropy rates of some of these chains. This leaves many natural problems open.

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Title: On ideals and associated notions of convergence
Speaker: Prof. Pratulananda Das, Jadavpur University, Kolkata.
Date: 08 March 2016
Time: 4 pm
Venue: LH-1

In this talk we discuss how the notion of usual convergence is extended using the notion of ideals and the importance of P-ideals. We then show how ideals can be generated and in particular how the P ideals can be generated by matrices other than regular summability matrix

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Title: Wild Topology, Group Theory and a conjecture in Number Theory
Speaker: Greg Conner, Brigham Young University
Date: 02 March 2016
Venue: LH-1, Department of Mathematics

One of the most useful analogies in mathematics is the fundamental group functor (also known as the Galois Correspondence) which sends a topological space to its fundamental group while at the same time sending continuous maps between spaces to corresponding homomorphisms of groups in such a way that compositions of maps are preserved.

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Title: Strong pseudoconvexity in Banach spaces and applications
Speaker: Sofia Ortega Castillo
Date: 19 February 2016
Venue: LH 3

Having been unclear how to widely define strong (or strict) pseudoconvexity in the infinite-dimensional context, we compared the concept in the smooth-boundary case with strict convexity. As a result, w= e accomplished establishing definitions of local uniform pseudoconvexity, uniform pseudoconvexity and strict pseudoconvexity for open and bounded subsets of a Banach space. We will see examples of Banach spaces with uniformly pseudoconvex unit ball, as well as examples of Banach spaces whose unit ball is not even strictly pseudoconvex. As an application of the techniques developed, we show that in finite dimension the concept of strict plurisubharmonicity coincides with strict plurisubharmonicity in distribution.

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Title: Operator theory on symmetrized bidisc and tetrablock - some explicit constructions
Speaker: Mr. Haripada Sau Ph. D. Research Scholar
Date: 12 February 2016
Time: 11.00 a.m.
Venue: Lecture Hall I, Dept of Mathematics

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Title: Goldman bracket : Centers, Geometric intersection numbers and Length equivalent curves.
Speaker: Mr. Arpan Kabiraj.
Date: 11 February 2016
Time: 10.00 a.m. - 11.00 a.m.
Venue: Lecture Hall I, Department of Mathematics, IISc.

In the 1980s, Goldman introduced a Lie algebra structure on the free vector space generated by the free homotopy classes of oriented closed curves in any orientable surface F. This Lie bracket is known as the Goldman bracket and the Lie algebra is known as the Goldman Lie algebra.

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Title: Funk and Hilbert geometry: Euclidean, non-Euclidean and timelike
Speaker: Athanase Papadopolous Universite de Strasbourg
Date: 04 February 2016
Venue: LH3 Math Dept IISc

I will present the Funk and Hilbert metrics on convex sets in the setting of Euclidean, non-Euclidean and timelike geometries. I will explain the motivation for studying these metrics and highlight some of their main properties, concerning geodesics, infinitesima structures and isometries.

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Title: On critical points of random polynomials and spectrum of certain products of random matrices
Speaker: Tulasi Ram Reddy A
Date: 27 January 2016
Time: 11:00 am
Venue: Lecture Hall 3, Department of Mathematics

In the first part we study critical points of random polynomials. We choose two deterministic sequences of complex numbers,whose empirical measures converge to the same probability measure in complex plane. We make a sequence of polynomials whose zeros are chosen from either of sequences at random. We show that the limiting empirical measure of zeros and critical points agree for these polynomials. As a consequence we show that when we randomly perturb the zeros of a deterministic sequence of polynomials, the limiting empirical measures of zeros and critical points agree. This result can be interpreted as an extension of earlier results where randomness is reduced. Pemantle and Rivin initiated the study of critical points of random polynomials. Kabluchko proved the result considering the zeros to be i.i.d. random variables.

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Title: The Batalin-Vilkovisky structure on a model of the loop space homology.
Speaker: Prof. Jean-Baptiste Gatsinzi, University of Namibia, Namibia.
Date: 22 January 2016
Time: 3 pm
Venue: LH-1

Let X be a closed, simply connected and orientable manifold of dimension m and LX the space of free loops on X. We use Rational Homotopy Theory to construct a model for the loop space homology. We further define a BV structure which is equivalent, in some cases, to the Chas-Sullivan BV operator.

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Title: Linking numbers for algebraic cycles
Speaker: Souvik Goswami (ICMAT, Madrid, Spain)
Date: 18 January 2016
Time: 4pm
Venue: LH-1

In algebraic geometry the concept of height pairing (a particular example

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Title: Upscaling of a System of Semilinear Diffusion‐Reaction Equations in a Heterogeneous Medium: Multi‐Scale Modeling and Periodic Homogenization.
Speaker: Hari Shankar Mahato (University of Georgia, USA)
Date: 10 January 2016
Time: 11 am
Venue: LH-1

A porous medium (concrete, soil, rocks, water reservoir, e.g.) is a multi‐scale medium

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Title: On some fourth order equations associated to Physics.
Speaker: Sanjiban Santra (CIMAT, Mexico)
Date: 05 January 2016
Time: 4pm
Venue: LH-1

We consider a fourth order traveling wave equation associated to the Suspension Bridge Problem (SBP). This equations are modeled by the traveling wave behavior on the Narrows Tacoma and the Golden Gate bridge. We prove existence of homoclinic solutions when the wave speed is small. We will also discuss the associated fourth order Liouville theorem to the problem and possible link with the De Giorgi’s conjecture. This is an attempt to prove the McKenna-Walter conjecture which is open for the last two decades.

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Title: Twin Primes
Speaker: M. Ram Murty, Queen's University, Kingston, Canada
Date: 04 January 2016
Time: 4pm
Venue: LH-1

There is a folklore conjecture that there are infinitely many primes p such that p+2 is also prime. This conjecture is still open. However, in the last two years, spectacular progress has been made to show that there are infinitely many primes p such that p+h is also prime with 1< h < 247. We will discuss the history of this problem and explain the new advances in sieve theory that have led to these remarkable results. We will also highlight what we may expect in the future.

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Title: A motivic formula for the $L$-function of an abelian variety over a function field
Speaker: Bruno Kahn, University of Paris VI
Date: 01 January 2016
Time: 4 pm
Venue: LH-1

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Title: Homogenization of Periodic Optimal Control Problems in a Domain with highly oscillating boundary
Speaker: Ravi Prakash, University of Conception, Chilie
Date: 18 December 2015
Time: 2:30pm
Venue: LH-3

Homogenization is a branch of science where we try to understand microscopic structures via a macroscopic medium. Hence, it has applications in various branches of science and engineering. This study is basically developed from material science in the creation of composite materials though the contemporary applications are much far and wide. It is a process of understanding the microscopic behavior of an in-homogeneous medium via a homogenized medium. Mathematically, it is a kind of asymptotic analysis. We plan to start with an illustrative example of limiting analysis in 1-D for a second order elliptic partial differential equation. We will also see some classical results in the case of periodic composite materials and oscillating boundary domain. The emphasis will be on the computational importance of homogenization in numerics by the introduction of correctors. In the second part of the talk, we will see a study on optimal control problems posed in a domain with highly oscillating boundary. We will consider periodic controls in the oscillating part of the domain with a model problem of Laplacian and try to understand their optimality and asymptotic behavior.

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Title: Topics in the history of Harmonic Analysis (6 lectures)
Speaker: G B Folland (University of Washington, Seattle)
Date: 16 December 2015
Time: 4pm
Venue: LH-1

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Title: Voevodsky's smash nilpotence conjecture
Speaker: Ronnie Sebastian (IISER Pune)
Date: 10 December 2015
Time: 4pm
Venue: LH-1

Voevodsky’s conjecture states that numerical and smash equivalence coincide for algebraic cycles. I shall explain the conjecture in more detail and talk about some of the examples for which this conjecture is known.

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Title: Enumerative Geometry of rational cuspidal curves on del-Pezzo surfaces.
Speaker: Ritwik Mukherjee (TIFR)
Date: 01 December 2015
Time: 4 pm
Venue: LH-1

Enumerative geometry is a branch of mathematics that deals with the following question: How many geometric objects are there that satisfy certain constraints? The simplest example of such a question is How many lines pass through two points?. A more interesting question is How many lines are there in three dimensional space that intersect four generic lines?. An extremely important class of enumerative question is to ask How many rational (genus 0) degree d curves are there in CP^2 that pass through 3d-1 generic points? Although this question was investigated in the nineteenth century, a complete solution to this problem was unknown until the early 90’s, when Kontsevich-Manin and Ruan-Tian announced a formula. In this talk we will discuss some natural generalizations of the above question; in particular we will be looking at rational curves on del-Pezzo surfaces that have a cuspidal singularity. We will describe a topological method to approach such questions. If time permits, we will also explain the idea of how to enumerate genus one curves with a fixed complex structure by comparing it with the Symplectic Invariant of a manifold (which are essentially the number of curves that are solutions to the perturbed d-bar equation).

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Title: Functional equation for Selmer groups
Speaker: Somnath Jha (IIT, Kanpur)
Date: 30 November 2015
Venue: LH-1

Interplay between arithmetic and analytic objects are some of the beautiful aspects of number theory. In this talk, we will discuss several examples of this.

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Title: Existence of Nash equilibrium for chance-constrained games
Speaker: Vikas Singh (Universite Paris-Sud)
Date: 26 November 2015
Time: 3:00 pm
Venue: LH1

We consider an n-player strategic game with finite action sets. The payoffs of each player are random variables. We assume that each player uses a satisficing payoff criterion defined by a chance-constraint, i.e., players face a chance-constrained game. We consider the cases where payoffs follow normal and elliptically symmetric distributions. For both cases we show that there always exists a mixed strategy Nash equilibrium of corresponding chance-constrained game.

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Title: Hecke algebras and the Langlands program
Speaker: Manish Mishra (Universitat Heidelberg)
Date: 17 November 2015
Time: 4pm
Venue: LH-1

Given an irreducible polynomial f(x) with integer coefficients and a prime number p, one wishes to determine whether f(x) is a product of distinct linear factors modulo p. When f(x) is a solvable polynomial, this question is satisfactorily answered by the Class Field Theory. Attempts to find a non-abelian Class Field Theory lead to the development of an area of mathematics called the Langlands program. The Langlands program, roughly speaking, predicts a natural correspondence between the finite dimensional complex representations of the Galois group of a local or a number field and the infinite dimensional representations of real, p-adic and adelic reductive groups. I will give an outline of the statement of the local Langlands correspondence. I will then briefly talk about two of the main approaches towards the Langlands program - the type theoretic approach relying on the theory of types developed by Bushnell-Kutzko and others; and the endoscopic approach relying on the trace formula and endoscopy. I will then state a couple of my results involving these two approaches.

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Title: Algorithms and complexity for Turaev-Viro invariants
Speaker: Jonathan Spreer, The University of Queensland, Australia
Date: 13 November 2015
Time: 4 pm
Venue: LH-1

The Turaev-Viro invariants are a powerful family of topological invariants for distinguishing between different 3-manifolds. They are invaluable for mathematical software, but current algorithms to compute them require exponential time. I will discuss this family of invariants, and present an explicit fixed-parameter tractable algorithm for arbitrary r which is practical—and indeed preferable—to the prior state of the art for real computation.

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Title: Exploring parameterised complexity in computational topology
Speaker: Benjamin A. Burton, The University of Queensland, Australia
Date: 12 November 2015
Time: 4:00 pm
Venue: LH 1

Exact computation with knots and 3-manifolds is challenging - many fundamental problems are decidable but enormously complex, and many major algorithms have never been implemented. Even simple problems, such as unknot recognition (testing whether a loop of string is knotted), or 3-sphere recognition (testing whether a triangulated 3-manifold is topologically trivial), have best-known algorithms that are worst-case exponential time.

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Title: Title: Landstad-Vaes theory for locally compact quantum groups
Speaker: Sutanu Roy (University of Ottawa, Canada)
Date: 06 November 2015
Time: 4 pm
Venue: LH-1

In the seventies of last century, Magnus Landstad characterised the coefficient C-algebra inside the multiplier algebra of a given crossed product C-algebra subject to an action of an Abelian locally compact group G. In 2005, Stefaan Vaes extended the Landstad theory for regular locally compact quantum groups. He gave strong indications that this is not possible for non-regular groups. In this talk I shall explain how Landstad-Vaes theory extends for non-regular groups. To this end we have to consider not necessary continuous, but measurable, actions of locally compact quantum groups. For regular locally compact quantum groups any measurable action is continuous, so our theory contains that of Landstad-Vaes. This is a joint work with Stanislaw Lech Woronowicz.

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Title: Nonequilibrium Markov processes conditioned on large deviations
Speaker: Raphael Chetrite (Universite Nice Sophia Antipolis)
Date: 05 November 2015
Time: 4:00 pm
Venue: LH-1

I will present a general approach for constructing a Markov process that describes the dynamics of a nonequilibrium process when one or more observables of this process are observed to fluctuate in time away from their typical values.

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Title: On Risk Concentration
Speaker: Prof. Marie Kratz, ESSEC Business School, CREAR (risk research center)
Date: 26 October 2015
Time: 2:15 - 3:15 p.m.
Venue: Lecture Hall I, Department of Mathematics

We study the local behavior of (extreme) quantiles of the sum of heavy-tailed random variables, to infer on risk concentration. Looking at the literature, asymptotic (for high threshold) results have been obtained when assuming (asymptotic) independence and second order regularly varying conditions on the variables. Other asymptotic results have been obtained in the dependent case when considering specific copula structures. Our contribution is to investigate on one hand, the non-asymptotic case (i.e. for any threshold), providing analytical results on the risk concentration for copula models that are used in practice, and comparing them with results obtained via Monte-Carlo method. On the other hand, when looking at extreme quantiles, we assume a multivariate second order regular variation condition on the vectors and provide asymptotic risk concentration results. We show that many models used in practice come under the purview of such an assumption and provide a few examples. Moreover this ties up related results available in the literature under a broad umbrella. This presentation is based on two joint works, one with M. Dacorogna and L. Elbahtouri (SCOR), the other with B. Das (SUTD).

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Title: Iwasawa theory and the Birch and Swinnerton-Dyer conjecture:
Speaker: Sujatha Ramdorai (University of British Columbia, Vancouver, Canada)
Date: 08 September 2015
Time: 2 pm
Venue: LH 2

The celebrated BSD conjecture predicts a deep and mysterious relationship between the algebraic rank of an elliptic curve defined over a number field and an arithmetic invariant arising front he L-function of the elliptic curve. More amazingly, it predicts an exact formula for the leading term of the L-function. Iwasawa theory has proven to be an effective tool in trying to explain the philosophy behind such a mysterious relationship and also in establishing the conjecture in certain cases. We shall outline this theory and discuss its applications.

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Title: Iwasawa theory and the Birch and Swinnerton-Dyer conjecture:
Speaker: Sujatha Ramdorai (University of British Columbia, Vancouver, Canada)
Date: 01 September 2015
Time: 2 pm
Venue: LH 2

The celebrated BSD conjecture predicts a deep and mysterious relationship between the algebraic rank of an elliptic curve defined over a number field and an arithmetic invariant arising front he L-function of the elliptic curve. More amazingly, it predicts an exact formula for the leading term of the L-function. Iwasawa theory has proven to be an effective tool in trying to explain the philosophy behind such a mysterious relationship and also in establishing the conjecture in certain cases. We shall outline this theory and discuss its applications.

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Title: Iwasawa theory and the Birch and Swinnerton-Dyer conjecture:
Speaker: Sujatha Ramdorai (University of British Columbia, Vancouver, Canada)
Date: 31 August 2015
Time: 2 pm
Venue: LH 2

The celebrated BSD conjecture predicts a deep and mysterious relationship between the algebraic rank of an elliptic curve defined over a number field and an arithmetic invariant arising front he L-function of the elliptic curve. More amazingly, it predicts an exact formula for the leading term of the L-function. Iwasawa theory has proven to be an effective tool in trying to explain the philosophy behind such a mysterious relationship and also in establishing the conjecture in certain cases. We shall outline this theory and discuss its applications.

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Title: Contact Structures and Contact Invariants in Heegaard Floer Homology.
Speaker: Dheeraj Kulkarni, RKMVU, Kolkata
Date: 31 August 2015
Time: 3:30 p.m
Venue: L-1, Department of Mathematics, IISc

There is a dichotomy of contact structures– tight vs overtwisted. Classification of overtwisted contact structures up to isotopy, due to Eliashberg, is well understood. However, there have been few results towards classification of tight contact structures. In general, given a contact structure it is difficult to know whether it is tight or not.

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Title: Iwasawa theory and the Birch and Swinnerton-Dyer conjecture:
Speaker: Sujatha Ramdorai (University of British Columbia, Vancouver, Canada)
Date: 25 August 2015
Time: 2 pm
Venue: LH 2

The celebrated BSD conjecture predicts a deep and mysterious relationship between the algebraic rank of an elliptic curve defined over a number field and an arithmetic invariant arising front he L-function of the elliptic curve. More amazingly, it predicts an exact formula for the leading term of the L-function. Iwasawa theory has proven to be an effective tool in trying to explain the philosophy behind such a mysterious relationship and also in establishing the conjecture in certain cases. We shall outline this theory and discuss its applications.

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Title: Localisation theorems for Bochner-Riesz means.
Speaker: Jotsaroop Kaur (University of Milano, Italy)
Date: 21 August 2015
Time: 4 pm
Venue: LH 1

Define $S_R^\alpha f := \int_{\mathbb{R}^d} (1-\frac{|\xi|^2}{R^2})_+^\alpha$ $\hat{f} (\xi) e^{i2\pi (x.\xi)} d\xi$, the Bochner Riesz means of order $\alpha \geq 0$. Let $f\in L^2(\mathbb{R}^d)$ and $f \neq 0$ in an open, bounded set $B.$ It is known that $S_R^\alpha f$ goes to 0 a.e. in $B$ as $R\rightarrow\infty.$ We study the pointwise convergence of Bochner Riesz means $S_{R}^\alpha f, \alpha>0$ as $R \rightarrow \infty$ on sets of positive Hausdorff measure in $\mathbb{R}^d$ by making use of the decay of the spherical means of Fourier Transform of fractal measures. We get an improvement in the range of the Hausdorff dimension of the sets on which it converges. When $0<\alpha<\frac{d-1}{4},$ we get the best possible result in $\mathbb{R}^2$ and in higher dimensions we improve the result by L.Colzani, G. Gigante and A. Vargas. Steins interpolation theorem also gives us the corresponding result for $f\in L^p(\mathbb{R}^d), 1<p<2.$

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Title: Gohberg Lemma, Compactness and Essential Spectrum of Operators on Compact Lie Groups
Speaker: Aparajita Dasgupta (EPFL, Lausanne)
Date: 20 August 2015
Time: 11 am
Venue: LH-1

In this talk we prove a version of the Gohberg lemma on compact Lie groups giving an estimate from below for the distance from a given operator to the set of compact operators on compact Lie groups. As a consequence, we prove several results on bounds for the essential spectrum and a criterion for an operator to be compact. The conditions are given in terms of the matrix-valued symbols of operators. (This is a joint work with Professor Michael Ruzhansky.)

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Title: AN INTRODUCTION TO ATLAS: BASIC BACKGROUND AND APPLICATIONS
Speaker: JONATHAN FERNANDES
Date: 14 August 2015
Time: 4pm
Venue: LH-1

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Title: Koszul duality theory for algebras.
Speaker: Anita Naolekar (ISI, Bengaluru)
Date: 12 August 2015
Time: 11 am
Venue: LH4

Koszul duality theory is a homological method aiming at constructing an explicit quasi-free resolution for quadratic algebras. We introduce the concepts of bar (and cobar) construction for a quadratic algebra (and coalgebra) and provide a quasi-free resolution for quadratic algebras, under certain assumptions.

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Title: Dual pairs and intertwining distributions
Speaker: Angela Pasquale (Universite de Lorraine)
Date: 10 August 2015
Time: 4pm
Venue: LH-1

A reductive dual pair in the group Sp(W) of isometries of a symplectic space W, over a local

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Title: Reflected Backward SDEs with General Jumps
Speaker: Youssef Oukine (Universite Cadi Ayyad, Maroc)
Date: 07 August 2015
Time: 3-4 pm
Venue: LH-1

In the first part of this paper we give a solution for the one-dimensional reflected backward stochastic differential equation (BSDE for short) when the noise is driven by a Brownian motion and an independent Poisson random measure. The reflecting process is right continuous with left limits (RCLL for short) whose jumps are arbitrary. We first prove existence and uniqueness of the solution for a specific coefficient in using a method based on a combination of penalization and the Snell envelope theory. To show the general result we use a fixed point argument in an appropriate space. The second part of the paper is related to BSDEs with two reflecting barriers. Once more we prove existence and uniqueness of the solution of the BSDE.

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Title: Operads: An Introduction.
Speaker: Anita Naolekar (ISI, Bengaluru)
Date: 05 August 2015
Time: 11 am
Venue: LH4

An operad is an algebraic device which encodes a type of algebra. The classical types of algebras, ie. associative, commutative and Lie algebras give the first examples of algebraic operads. Operadic point of view has several advantages. Firstly, many results known for classical algebras, when written out in operadic language, can be applied to other types of algebras. Secondly, operadic language simplifies the statements and proofs. Thirdly, even for classical cases, operad theory has provided new results. We start with several equivalent definitions, together with examples, and few basic properties.

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Title: On critical points of random polynomials and spectrum of certain products of Ginibre matrices.
Speaker: Tulasi Ram Reddy A
Date: 24 July 2015
Time: 11:00 am
Venue: Lecture Hall I, Department of Mathematics

In the first part we study critical points of random polynomials. We choose two deterministic sequences of complex numbers, whose empirical measures converge to the same probability measure in complex plane. We make a sequence of polynomials whose zeros are chosen from either of sequences at random. We show that the limiting empirical measure of zeros and critical points agree for these polynomials. As a consequence we show that when we randomly perturb the zeros of a deterministic sequence of polynomials, the limiting empirical measures of zeros and critical points agree. This result can be interpreted as an extension of earlier results where randomness is reduced. Pemantle and Rivin initiated the study of critical points of random polynomials. Kabluchko proved the result considering the zeros to be i.i.d. random variables.

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Title: Finite configurations in sparse sets
Speaker: Professor Malabika Pramanik University of British Columbia, Vancouver
Date: 22 July 2015
Time: 11:30 am
Venue: LH-1

A problem of interest in geometric measure theory both in discrete and continuous settings is the identification of algebraic and geometric patterns in thin sets. The first two lectures will be a survey of the literature on pattern recognition in sparse sets, with a greater emphasis on continuum problems. The second two contain an exposition of recent work, joint in part with Vincent Chan, Kevin Henriot and Izabella Laba on the existence of linear and polynomial configurations in multi-dimensional Lebesgue-null sets satisfying appropriate Hausdorff and Fourier dimensionality conditions.

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Title: Some computational and analytic aspects of Chern-Weil forms
Speaker: Vamsi Pingali (Johns Hopkins University)
Date: 02 July 2015
Time: 4-5 pm
Venue: LH1

This talk will focus on two aspects of vector bundles. One is the calculation and application of certain characteristic and secondary characteristic forms (i.e. Chern, Chern-Simons, and Bott-Chern forms). This part is joint work with Leon Takhtajan and Indranil Biswas. The second is to study certain fully nonlinear PDE akin to the Monge-Amp\\‘ere equation arising from these differential geometric objects. An existence result or two will be presented along with the difficulties involved in the PDE. Moreover, other areas of geometry and physics from which the same PDE arise will be pointed out.

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Title: Fast algorithms for data analysis and elliptic partial differential equations
Speaker: Sivaram Ambikasaran (NYU)
Date: 24 June 2015
Time: 11-12
Venue: LH1

Large-dense matrices arise in numerous applications: boundary integral formulation for elliptic partial differential equations, covariance matrices in statistics, inverse problems, radial basis function interpolation, multi frontal solvers for sparse linear systems, etc. As the problem size increases, large memory requirements, scaling as O(N^2), and extensive computational time to perform matrix algebra, scaling as O(N^2) or O(N^3), make computations impractical. I will discuss some novel methods for handling these computationally intense problems. In the first half of the talk, I will discuss my contributions to some of the new developments in handling large dense covariance matrices in the context of computational statistics and Bayesian data assimilation. More specifically, I will be discussing how fast dense linear algebra (O(N) algorithms for inversion, determinant computation, symmetric factorisation, etc.) enables us to handle large scale Gaussian processes, thereby providing an attractive approach for big data applications. In the second half of the talk, I will focus on a new algorithm termed Inverse Fast Multipole Method, which permits solving singular integral equations arising out of elliptic PDE’s at a computational cost of O(N).

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Title: Electrostatic skeletons
Speaker: Koushik Ramachandran (ISI, Bangalore)
Date: 24 June 2015

Let P be the equilibrium potential of a compact set K in R^n. An electrostatic skeleton of K is a positive measure such that the closed support S of has connected complement and empty interior, and the Newtonian (or logarithmic, when n = 2) potential of is equal to P near infinity. We prove the existence and uniqueness of an electrostatic skeleton for any simplex. – This message has been scanned for viruses and dangerous content by MailScanner, and is believed to be clean.

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Title: Small Combination of Slices in Banach Spaces
Speaker: Dr. Sudeshna Basu (George Washington University)
Date: 10 June 2015
Time: 3.00 p.m.
Venue: LH I, Department of Mathematics

Abstract : In this work, we study certain stability results for Ball Separationproperties in Banach Spaces leading to a discussion in the context of operator spaces. In this work, we study certain stability results for Small Combination of Slices Property (SCSP) leading to a discussion on SCSP in the context of operator spaces. SCSpoints were first introduced as a slice generalisation of the PC (i.e. point ofcontinuity points for which the identity mapping from weak topology to normtopology is continuous.) It is known that X is strongly regular respectively Xis w-strongly regular) if and only if every non empty bounded convex set K in X ( respectively K in X) is contained in the norm closure ( respectively w- closure)of SCS(K)( respectively w-SCS(K)) i.e. the SCS points ( w- SCS points) of K. Later, it was proved that a Banach space has Radon- Nikodym Property (RNP) if and only if it is strongly regular and it has the Krein-Milamn Property(KMP). Subsequently, the concepts of SCS points was used to investigate the structure of non-dentable closed bounded convex sets in Banach spaces. The point version of the result was also shown to be true .

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Title: Random Matrices, Numerical Computation, and Applications
Speaker: Alan Edelman (MIT)
Date: 03 June 2015
Time: 4-5 pm
Venue: LH1

This talk is about random matrix theory. Linear Algebra and maybe a little probability are the only prerequisites. Random matrix theory is now finding many applications. Many more applications remain to be found. It is truly matrix statistics, when traditional statistics has been primarily scalar and vector statistics. The math is so much richer, and the applications to computational finance, HIV research, the Riemann Zeta Function, and crystal growth, to name a few, show how important this area is. I will show some of these applications, and invite you to find some of your own.

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Title: Automated theorem proving using Learning : concepts and code
Speaker: Siddhartha Gadgil
Date: 15 May 2015
Time: 11:00 a.m.
Venue: LH-III, Department of Mathematics, IISc

In this very informal seminar, I will discuss various aspects of ongoing work to build an automated theorem proving system using, among other things, machine learning.

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Title: Equivariant Cobordism Classes of Milnor Manifolds
Speaker: Swagata Sarkar ISI Kolkata
Date: 28 April 2015
Time: 11:00 a.m. - 12:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Let G be a 2-group, and let Z(G) denote the equivariant cobordism algebra of G-manifolds with finite stationary point sets.A cobordism class in Z(G) is said to be indecomposable if it cannot be expressed as the sum of products of lower dimensional cobordism classes.Indecomposable classes generate the cobordism algebra Z(G). We discuss a sufficient criteria for indecomposability of cobordism classes. Using the above mentioned criterion, we show that the classes of Milnor manifolds (i.e., degree 1 hypersurfaces of the product of two real projective spaces) give non-trivial, indecomposable elements in Z(G) in degrees up to 2^n - 5. This talk is based on joint work with Samik Basu and Goutam Mukherjee.

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Title: $L^p$-Asymptotics of Fourier transform of fractal measures
Speaker: K. S. Senthil Raani
Date: 23 April 2015
Time: 3:00pm - 4:00pm
Venue: Lecture Hall I, Department of Mathematics

One of the basic questions in harmonic analysis is to study the decay properties of the Fourier transform of measures or distributions supported on thin sets in $\\R^n$. When the support is a smooth enough manifold, an almost complete picture is available. One of the early results in this direction is the following: Let $f\\in C_c^{\\infty}(d\\sigma)$, where $d\\sigma$ is the surface measure on the sphere $S^{n-1}\\subset\\R^n$. Then

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Title: Linearity in perceptual space
Speaker: S. P. Arun
Date: 10 April 2015
Time: lecture i: 2:15 pm. to 3:15 p.m. coffee : 3:15 p.m. to 3:30 p.m. lecture ii: 3:30 p.m. to 4: 30 p.m. high tea: 4:30 p.m.
Venue: LH-I, Department of Mathematics, IISc.

Our vision is unsurpassed by machines because we use a sophisticated object representation. This representation is unlike the retinal image: on the one hand, two out-of-phase checkerboards, maximally different in image pixels, appear perceptually similar. On the other hand, two faces, similar in their image pixels, appear perceptually distinct. What is then the nature of perceptual space? Are there principles governing its organization? To address these questions, we have been using visual search to measure similarity relations between objects. I will summarize a line of research from our laboratory indicative of a surprising linear rule governing distances in perceptual space. In the first study, we found that search time is inversely proportional to the feature difference between the target and distracters. The reciprocal of search time is therefore linear and interestingly, it behaved like a mathematical distance metric. It also has a straightforward interpretation as a saliency signal that drives visual search (Arun, 2012). In a second study, complex searches involving multiple distracters were explained by a linear sum of pair-wise dissimilarities measured from simpler searches involving homogeneous distracters (Vighneshvel & Arun, 2013). In a third study, dissimilarities between objects differing in multiple features were found to combine linearly. This was also true for integral features such as the length and width of a rectangle upon including aspect ratio as an additional feature (Pramod & Arun, 2014). Finally, I will describe some recent results extending these findings to more naturalistic objects.

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Title: Achieving positive information velocity in wireless networks
Speaker: Srikanth Iyer (IISc, Bangalore)
Date: 06 April 2015
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

In wireless networks, where each node transmits independently of other nodes in the network (the ALOHA protocol), the expected delay experienced by a packet until it is successfully received at any other node is known to be infinite for signal-to-interference-plus-noise-ratio (SINR) model with node locations distributed according to a Poisson point process. Consequently, the information velocity, defined as the limit of the ratio of the distance to the destination and the time taken for a packet to successfully reach the destination over multiple hops, is zero, as the distance tends to infinity. A nearest neighbor distance based power control policy is proposed to show that the expected delay required for a packet to be successfully received at the nearest neighbor can be made finite. Moreover, the information velocity is also shown to be non-zero with the proposed power control policy. The condition under which these results hold does not depend on the intensity of the underlying Poisson point process.

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Title: Factorization of holomorphic eta quotients
Speaker: Soumya Bhattacharya CIRM Trento, Italy
Date: 20 March 2015
Time: 2:00 p.m. - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Unlike integer factorization, a reducible holomorphic eta quotient may not factorize uniquely as a product of irreducible holomorphic eta quotients. But whenever such an eta quotient is reducible, the occurrence of a certain type of factor could be observed: We conjecture that if a holomorphic eta quotient f of level M is reducible, then f has a factor of level M. In particular, it implies that rescalings and Atkin-Lehner involutions of irreducible holomorphic eta quotients are irreducible. We prove a number of results towards this conjecture: For example, we show that a reducible holomorphic eta quotient of level M always factorizes nontrivially at some level N which is a multiple of M such that rad(N) = rad(M) and moreover, N is bounded from above by an explicit function of M. This implies a new and much faster algorithm to check the irreducibility of holomorphic eta quotients. In particular, we show that our conjecture holds if M is a prime power. We also show that the level of any factor of a holomorphic eta quotient f of level M and weight k is bounded w.r.t. M and k. Further, we show that there are only finitely many irreducible holomorphic eta quotients of a given level and provide a bound on the weights of such eta quotients. Finally, we give an example of an infinite family of irreducible holomorphic eta quotients of prime power levels.

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Title: Arithmetic of Farey-Ford Packings
Speaker: Amita Malik University of Illinois at Urbana-Champaign
Date: 18 March 2015
Time: 3:30 p.m. - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

Farey-Ford Packings are a special case of more general circle packings called Apollonian Circle Packings (ACP). These packings have some very interesting properties, for exmaple, if any four mutually tangent circles have integer curvatures, then so do all others in the packing. This has led to many important problems like prime number theorem in this setting. Kontorovich and Oh explore it from dynamics point of view whereas Bourgain, Fuchs and Sarnak look at them more number theoretically. In this talk, our focus will be on the specialized packings Farey-Ford Packings. We consider some basic statistics associated to these circles and answer some questions about their distributions and asymptotic behavior. One can ask similar questions in the general setting for ACP, and if time permits, we will discuss it in this talk. Some of this is joint work with Athreya, Chaubey and Zaharescu.

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Title: Index theory and the Arveson Conjecture
Speaker: Ronald G. Douglas Texas A&M University
Date: 13 March 2015
Time: 3:30 p.m. - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

TBA

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Title: Composition Operators on Modulation Spaces and Application to Nonlinear Schrodinger Equation
Speaker: P.K. Ratnakumar HRI, Allahabad
Date: 12 March 2015
Time: 3:30 p.m. - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

TBA

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Title: Computational Aspects of Burnside Algebras II
Speaker: Prof. Dr. Martin Kreuzer University of Passau, Germany
Date: 02 March 2015
Time: 2:00 p.m. - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

In this two-part talk, we reconsider Burnside algebras, a classical tool in the theory of finite groups, from a computational perspective. Using modern computer algebra systems, many of the results about these rings that were proved in the second half of the last century can be transformed into effective algorithms.

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Title: Computational Aspects of Burnside Algebras I
Speaker: Prof. Dr. Martin Kreuzer University of Passau, Germany
Date: 25 February 2015
Time: 2:00 p.m. - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

In this two-part talk, we reconsider Burnside algebras, a classical tool in the theory of finite groups, from a computational perspective. Using modern computer algebra systems, many of the results about these rings that were proved in the second half of the last century can be transformed into effective algorithms.

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Title: Prescribing Gauss curvature using mass transport
Speaker: Jerome Bertrand Universit Paul Sabatier, Toulouse, France
Date: 25 February 2015
Time: 3:30 p.m. - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

In this talk, I will give a proof of Alexandrovs theorem on the Gauss curvature prescription of Euclidean convex body. The proof is mainly based on mass transport. In particular, it doesnt rely on pdes method nor convex polyhedra theory. To proceed, I will discuss generalizations of well-known results for the quadratic cost to the case of a cost function which assumes infinite value.

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Title: Axioms of Adaptivity
Speaker: Prof Carsten Carstensen Humboldt University, Berlin
Date: 23 February 2015
Time: 11:00 a.m. - 12:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Four axioms (A1)–(A4) link estimators and distance functions on a set of admissible refinements together and imply optimality of a standard finite element routine on an abstract level with a loop: solve, estimate, mark, and refine. The presentation provides proofs and examples of the recent review due to C. Carstensen, M. Feischl, M. Page, and D. Praetorius: The axioms of adaptivity, Comput. Math. Appl. 67 (2014) 1195 –1253 and so discusses the current literature on the mathematics of adaptive finite element methods. The presentation concludes with an overview over several applications of the set of axioms. If time permits, some recent developments are discussed on ongoing joint work with Hella Rabus on separate marking.

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Title: The dimer model and generalisations
Speaker: Arvind Ayyer
Date: 20 February 2015
Time: lecture i: 2:15 - 3:15 p.m. coffee break: 3:15 p.m. - 3:30 p.m. lecture ii: 3:30 - 4:30 p.m. high tea: 4:30 p.m.
Venue: LH-I, Department of Mathematics, IISc.

In the first half of the talk, I will define the dimer model on planar graphs and prove Kasteleyn’s groundbreaking result expressing the partition function (i.e. the generating function) of the model as a Pfaffian. I will then survey various results arising as a consequence, culminating in the beautiful limit shape theorems of Kenyon, Okounkov and coworkers.

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Title: What is Quantum Stochastic Calculus?
Speaker: Prof K. R. Parthasarthy ISI Delhi
Date: 13 February 2015
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

TBA

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Title: Indeterminate moment problems and growth of associated entire functions
Speaker: Prof Christian Berg University of Copenhagen
Date: 06 February 2015
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

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Title: Weighted norm inequalities for Weyl multipliers and Hermite pseudo-multipliers
Speaker: Sayan Bagchi
Date: 30 January 2015
Time: 2:30pm - 3:30pm
Venue: Lecture Hall I, Department of Mathematics

In this talk we deal with two problems in harmonic analysis. In the first problem we discuss weighted norm inequalities for Weyl multipliers satisfying Mauceri’s condition. As an application, we prove certain multiplier theorems on the Heisenberg group and also show in the context of a theorem of Weis on operator valued Fourier multipliers that the R-boundedness of the derivative of the multiplier is not necessary for the boundedness of the multiplier transform. In the second problem we deal with a variation of a theorem of Mauceri concerning the L^p boundedness of operators M which are known to be bounded on L^2: We obtain sufficient conditions on the kernel of the operator M so that it satisfies weighted L^p estimates. As an application we prove L^p boundedness of Hermite pseudo-multipliers.

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Title: On applying the Deligne-Kazhdan philosophy to classical groups
Speaker: Sandeep Varma TIFR, Mumbai
Date: 29 January 2015
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

I will report on work in progress with Radhika Ganapathy. One wishes to study irreducible smooth' complex representations of symplectic and (split) orthogonal groups over local function fields, i.e., fields of the form F_q((t)). The theory of close local fields’ proposes to do this by studying the representation theory of these groups over (varying) finite extensions of Q_p. We will discuss an approach to using this philosophy to study the local Langlands correspondence for these groups.

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Title: Some qualitative uncertainty principles revisited
Speaker: Alladi Sitaram
Date: 16 January 2015
Time: 2:30 - 3:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

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Title: Some qualitative uncertainty principles revisited
Speaker: Alladi Sitaram IISc
Date: 16 January 2015
Time: 2:30 - 3:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

TBA

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Title: Geometry of algebraic surfaces and holomorphic convexity
Speaker: B. P. Purnaprajna University of Kansas
Date: 09 January 2015
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

TBA

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Title: Some qualitative uncertainty principles revisited
Speaker: Alladi Sitaram IISc
Date: 09 January 2015
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

TBA

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Title: Lengths of Monotone Subsequences in a Mallows Permutation
Speaker: Nayantara Bhatnagar (University of Delaware)
Date: 05 January 2015
Time: 2:00 pm
Venue: LH-1, Department of Mathematics, IISc

The longest increasing subsequence (LIS) of a uniformly random permutation is a well studied problem. Vershik-Kerov and Logan-Shepp first showed that asymptotically the typical length of the LIS is 2sqrt(n). This line of research culminated in the work of Baik-Deift-Johansson who related this length to the Tracy-Widom distribution.

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Title: Iwasawa theory
Speaker: Mahesh Kakde King's College London
Date: 05 January 2015
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall III, Department of Mathematics

I will start with an overview of classical Iwasawa theory and give a formulation of main conjectures in noncommutative Iwasawa theory. If time permits I will say something about proof of main conjectures in non-commutative Iwasawa theory.

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Title: Zagier polynomials and modified N\{o}rlund polynomials
Speaker: Atul Dixit Tulane University, LA
Date: 23 December 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

In 1998, Don Zagier studied the ‘modified Bernoulli numbers’ $B_n^{*}$ whose 6-periodicity for odd $n$ naturally arose from his new proof of the Eichler-Selberg trace formula. These numbers satisfy amusing variants of the properties of the ordinary Bernoulli numbers. Recently, Victor H. Moll, Christophe Vignat and I studied an obvious generalization of the modified Bernoulli numbers, which we call ‘Zagier polynomials’. These polynomials are also rich in structure, and we have shown that a theory parallel to that of the ordinary Bernoulli polynomials exists. Zagier showed that his asymptotic formula for $B_{2n}^{*}$ can be replaced by an exact formula.

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Title: On splitting of primes and simple extensions of integrally closed domains
Speaker: Sudesh Khanduja IISER Mohali
Date: 15 December 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

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Title: Homogenization of a system of multi-species semilinear diff usion - reaction equations and moving boundary problems
Speaker: Dr. Hari Shankar Mahato University of Erlangen-Nrnberg
Date: 08 December 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

A porous medium (concrete, soil, rocks, water reservoir, e.g.) is a multiscale medium where the heterogeneities present in the medium are characterized by the micro scale and the global behaviors of the medium are observed by the macro scale. The upscaling from the micro scale to the macro scale can be done via averaging methods.

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Title: Rational loop space homology of homogeneous spaces
Speaker: Jean-Baptiste Gatsinzi University of Namibia
Date: 05 December 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

We recall some facts about Rational Homotopy Theory, from both Sullivan and Quillen points of view. We show how to find a Sullivan model of a homogeneous space G/H . Let M be a closed oriented smooth manifold of dimension d and LM= map(S^1, M) denote the space of free loops on M . Using intersection products, Chass and Sullivan defined a product on \\mathbb{H}*(LM)=H{+d} (LM) that turns to be a graded commutative algebra and defined a bracket on \\mathbb{H}_(LM) making of it a Gerstenhaber algebra. From the work of Jones, Cohen, F\\‘elix, Thomas and others there is an isomorphism of Gerstenhaber algebras between the Hochschild cohomology HH^(C^(M), C^(M)) and \\mathbb{H}_(LM) . Using a Sullivan model (\\land V, d) of M , we show that that the Gerstenhaber bracket can be computed in terms of derivations on (\\land V, d) . Precisely, we show that HH^(\\land V, \\land V) is isomorphic to H_(\\land(V)\\otimes \\land Z , D) , where Z is the dual of V . We will illustrate with computations for homogeneous spaces.

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Title: Optimal differentiation on arbitrary grids
Speaker: Divakar Viswanath (University of Michigan)
Date: 24 November 2014
Time: 2:00 pm
Venue: LH-1, Department of Mathematics, IISc

Finite difference formulas approximate the derivatives of a function given its values at a discrete set of grid points. Much of the theory for choosing grid points is concerned with discretization errors and rounding errors are ignored completely. However, when the grids become fine the rounding errors dominate. Finding finite difference formulas which optimize the total error leads to a combinatorial optimization problem with a large search space. In this talk, we will describe a random walk based strategy for tackling the combinatorial optimization problem.

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Title: Statistics in the Anderson Model
Speaker: Prof. Krishna Maddaly IMSc
Date: 19 November 2014
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

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Title: Knots, algorithms and linear programming: the quest to solve unknot recognition in polynomial time
Speaker: A/Prof. Benjamin A. Burton, School of Mathematics and Physics, The University of Queensland, Brisbane, Australia
Date: 07 November 2014
Time: lecture i: 2:15 - 3:15 p.m. coffee break: 3:15 p.m. - 3:30 p.m. lecture ii: 3:30 - 4:30 p.m. high tea: 4:30 p.m.
Venue: LH-I, Department of Mathematics, IISc.

In this talk we explore new approaches to the old and difficult computational problem of unknot recognition. Although the best known algorithms for this problem run in exponential time, there is increasing evidence that a polynomial time solution might be possible. We outline several promising approaches, in which computational geometry, linear programming and greedy algorithms all play starring roles.

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Title: From Calculus to Number Theory (via Cohomology)
Speaker: Professor A. Raghuram Indian Institute of Science Education and Research (IISER) Pune, Maharashtra, India
Date: 16 October 2014
Time: 4:00 pm to 5:00 pm
Venue: Lecture Hall III, Ground Floor, Department of Mathematics, IISc, Bangalore

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Title: The BNS invariant and its application to twisted conjugacy
Speaker: Prof. Parameswaran Sankaran IMSc
Date: 14 October 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

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Title: Riesz potentials and Sobolev embedding theorems
Speaker: Dr Rahul Garg Technion, Haifa, Israel
Date: 23 September 2014
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

I shall begin with the mapping properties of classical Riesz potentials acting on $L^p$-spaces. After reviewing the literature, I shall present our new ‘‘almost’’ Lipschitz continuity estimates for these and related potentials (including, for instance, the logarithmic potential) in the so-called supercritical exponent. Finally, I shall show how one could apply these estimates to deduce Sobolev embedding theorems. This is joint work with Daniel Spector and is available on arXiv:1404.1563.

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Title: An interesting result about finite dimensional complex semi-simple algebras
Speaker: Srikanth Tupurani IMSc
Date: 22 September 2014
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

I will prove the following interesting result about finite dimensional complex semi-simple algebra. Let A be a finite-dimensional complex semi-simple algebra without an M_{2}(C) summand and let S be an involutive unital C-algebra anti-automorphism of A. Then there exists an element a in A such that a and S(a) generate A as an algebra. In the proof I will use some basic results in linear algebra

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Title: Derived Category of N-complexes
Speaker: Samarpita Ray IISc
Date: 22 September 2014
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

The notion of N-complexes goes back to a 1996 preprint of Kapranov, in which he considered chains of composable morphisms satisfying d^N = 0 (as opposed to the usual $d^2 = 0$ which gives the usual chain complexes). Later on, much of the usual homological algebra for chain complexes (homotopy of morphisms, spectral sequences, etc) was generalized to N-complexes, mostly by Dubois-Violette. Recently in 2014 there has been a burst of interest in this topic with work of Iyama,Kato,Miyachi defining the corresponding N-derived category. We shall begin the talk with simple definitions of $N$ complexes and their homology groups. Then gradually we will move to the paper of Iyama explaining derived category of $N$-complexes.

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Title: HARMONIC ANALYSIS ON EXPONENTIAL HOMOGENEOUS SPACES AND DIFFERENTIAL OPERATORS
Speaker: Ali Baklouti University of Sfax, Sfax, Tunisia
Date: 02 September 2014
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

See http://www.math.iisc.ernet.in/~arvind/Baklouti-Abst.Bangalore14.pdf

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Title: On a theorem of Titchmarsh
Speaker: Radouan Daher University of Hassan II, Casablanca, Morocco.
Date: 26 August 2014
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

In this talk we discuss about the Fourier transforms of functions satisfying Lipschitz conditions of certain order. We cover Fourier transforms on Euclidean spaces, non compact symmetric spaces and also certain hyper groups.

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Title: Dynamics via quasi-homomorphisms
Speaker: Siddhartha Gadgil IISc
Date: 22 August 2014
Time: 11:00 a.m. - 12:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

In dynamics, one studies properties of a map from a space to itself, up to change of coordinates in the space. Hence it is important to understand invariants of the map under change of coordinates. An important such invariant is Poincare’s rotation number, associated to invertible maps from the circle to itself. Ghys and others have abstracted the rotation number to give many other important invariants of dynamical systems by viewing it in terms of so called quasi-homomorphisms. Quasi-homomorphisms are like homomorphisms, except that a bounded error is allowed in the definition. In this expository lecture I will introduce quasi-homomorphisms and show some interesting properties, constructions and application, including an alternative construction of the real numbers (due to Ross Street). I shall then show how these can be used to construct dynamical invariants, in particular the rotation number. Only basic algebra and analysis are needed as background for this lecture.

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Title: The Littlewood-Offord and related problems
Speaker: Manjunath Krishnapur
Date: 22 August 2014
Time: lecture i: 2:15-3:15 p.m. coffee break 3:15 p.m. -3:30 p.m. lecture ii: 3:30-4:30 p.m. high tea: 4:30 p.m.
Venue: LH-I, Department of Mathematics, IISc.

Given n non-zero real numbers v_1,…,v_n, what is the maximum possible number of subsets {i_1,…,i_k} that can have the same subset sum v_{i_1}+…+v_{i_n}? Littlewood and Offord raised the question, showed that the answer is at most 2^nlog(n)/\\sqrt{n} and conjectured that the log(n) can be removed. Erdos proved the conjecture and raised more questions that have continued to attract attention, primarily relating the arithmetic structure of v_1,…,v_n and the maximum number of subsets with a given subset-sum.

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Title: Computational representation theory of finite monoids
Speaker: Professor Nicolas M Thiery Laboratoire De Research En Informatique, Universite, Paris
Date: 20 August 2014
Time: 3:30 pm to 4:30 pm
Venue: Lecture Hall I, First Floor, Department of Mathematics, IISc

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Title: Crystal approach to affine Schubert calculus
Speaker: Professor Anne Schilling Department of Mathematics University of California USA
Date: 20 August 2014
Time: 2:00 pm to 3:00 pm
Venue: Lecture Hall I, First Floor, Department of Mathematics, IISc

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Title: Semigroups and Harmonic Analysis
Speaker: Luz Roncal Universidad de La Rioja, Logrono, Spain
Date: 19 August 2014
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

By using the language of diffusion semigroups, it is possible to define and study classical operators in harmonic analysis. We introduce and develop this idea, and show two applications. First, we investigate fractional integrals and Riesz transforms in compact Riemannian spaces of rank one. Secondly, we carry out the study of operators associated with a discrete Laplacian, namely the fractional Laplacian, maximal heat and Poisson semigroups, square functions, Riesz transforms and conjugate harmonic functions.

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Title: Asymptotic behavior of positive harmonic functions in some unbounded domains
Speaker: Subhroshekhar Ghosh (Princeton)
Date: 18 August 2014
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

This talk will concern asymptotic estimates at infinity for positive harmonic functions in a large class of non-smooth unbounded domains. These are domains whose sections, after rescaling, resemble a Lipschitz cylinder or a Lipschitz cone, e.g., various paraboloids and horns. We will also mention a few related results in probability, e.g harmonic measure (distribution of exit position of Brownian motion) estimates.

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Title: HARISH-CHANDRA ( 1923 - 1983 )
Speaker: Prof. Alladi Sitaram IISc
Date: 07 August 2014
Time: (1) 2:00 - 2:45 p.m. (2) 3:15 - 4:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Harish-Chandra is a mathematician whose name in the history of mathematics is permanently etched in stone. I will begin by giving a brief account of his life, and in the second half of the lecture, explain some of the technical terms used in the first half. This lecture is aimed mainly at Ph.D. students.

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Title: Vector-valued weighted inequalities for one-sided maximal functions
Speaker: Saurabh Kumar Srivastava IISER Bhopal
Date: 05 August 2014
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

In this talk we shall briefly discuss the theory of one-sided maximal functions. One-sided maximal function is a variant of the classical Hardy-Littlewood maximal function. The theory of one-sided maximal functions is an active research area. Specially, in the past two decades there has been a lot of research activities in this area.

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Title: Towards Rigorous Factoring
Speaker: Dr. Ramarathnam Venkatesan Principal Researcher, Microsoft Research
Date: 31 July 2014
Time: 4:00 pm
Venue: CSA Seminar Hall (Room No. 254, First Floor)

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Title: Homogenization of quasilinear parabolic problems by the method of Rothe and two scale convergence
Speaker: Emmanuel Kwame Essel University of Cape Coast, Ghana
Date: 30 July 2014
Time: 11:30a.m. - 12:30 p.m.
Venue: Lecture Hall V, Department of Mathematics

In this talk we consider a linear parabolic problem with time dependent coefficients oscillating rapidly in the space variable. The existence and uniqueness results are proved by using Rothe’’s method combined with the technique of two-scale convergence. Moreover, we derive a concrete homogenization algorithm for giving a unique and computable approximation of the solution.

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Title: HOMOTOPY AND HOMOLOGY OF NONCOMMUTATIVE SPACES
Speaker: Snigdhayan Mahanta University of Muenster
Date: 28 July 2014
Time: 3:30 - 4:30pm
Venue: Lecture Hall V, Department of Mathematics

In noncommutative geometry (NCG) one typically treats unital C-algebras as noncommutative compact spaces via Gelfand-Naimark duality. In various applications of NCG to problems in geometry or topology it is customary to first reformulate these problems in terms of certain (co)homology theories for noncommutative spaces. The celebrated Baum-Connes conjecture, that reduces the Novikov conjecture to an assertion in bivariant K-theory, is a prime example of this principle. However, the category of C-algebras is well-known to be de ficient from the viewpoint of homotopy theory or index theory. In this talk I am going to first survey certain (co)homology theories for noncommutative spaces, then present my proposed solution to the aforementioned problem, and finally (time permitting) discuss some applications. I will try to keep it non-technical and accessible to a wide range of audience.

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Title: A transference result between radial Fourier multipliers and zonal multipliers on the unit sphere.
Speaker: Sriram Alladi
Date: 24 July 2014
Time: 4:00 pm
Venue: LH-1

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Title: Non-backtracking spectrum of random graphs
Speaker: Charles Bordenave Universite de Toulouse
Date: 24 July 2014
Time: 11:30a.m. - 12:30 p.m.
Venue: Lecture Hall III, Department of Mathematics

The non-backtracking matrix of a graph is a non-symmetric matrix on the oriented edge of a graph which has interesting algebraic properties and appears notably in connection with the Ihara zeta function and in some generalizations of Ramanujan graphs. It has also be proposed recently in the context of community detection. In this talk, we will study the largest eigenvalues of this matrix for the Erdos-Renyi graph G(n,c/n) and other simple inhomogeneous random graphs. This is a joint work with Marc Lelarge and Laurent Maussouli.

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Title: Mechanisation of Knot Theory
Speaker: T. V. H. Prathamesh IISc
Date: 22 July 2014
Time: 11:00am - 12:00pm
Venue: Lecture Hall III, Department of Mathematics

Mechanisation of Mathematics refers to use of computers to generate or check proofs in Mathematics. It involves translation of relevant mathematical theories from one system of logic to another, to render these theories implementable in a computer. This process is termed formalisation of mathematics. Two among the many way of mechanising are: (1) generating results using Automated Theorem Provers, (2) Interactive theorem proving in a Proof Assistant which involves a combination of user intervention and automation.

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Title: Holonomy fibers of complex projective structures
Speaker: Subhojoy Gupta Caltech
Date: 17 July 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall III, Department of Mathematics

As a sequel to the talk on July 16th, I shall talk about a recent result (joint work with Shinpei Baba) concerning fibers of the holonomy map from P(S) to the PSL(2,C) character variety. The proof involves some three-dimensional hyperbolic geometry, and train-tracks.

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Title: On the rank of symmetric random matrices
Speaker: Rahul Roy ISI, Delhi
Date: 17 July 2014
Time: 11:30 - 12:30 p.m.
Venue: Lecture Hall III, Department of Mathematics

We discuss the question of rank of symmetric and non-symmetric matrices when the entries are i.i.d. non-degenerate random variables. In particular we show that for an $n \\times n$ symmetric matrix the probability that it is singular is of the order $O(n^{- (1/4) + \\epsilon}$. This is joint work with Paulo Manrique and Victor Perez-Abreu.

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Title: The Beginnings of Mathematics in India
Speaker: P. P. Divakaran CMI
Date: 17 July 2014
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

As in other ancient civilisations, mathematics in India began in counting and drawing: numbers and plane geometry. The earliest textually recorded geometry is that of the Sulbasutra (around 800 BC onwards) which are manuals for the construction of Vedic altars, its mathematical high point being the `theorem of the diagonal’, Pythagoras’ theorem to you and me. I will state its earliest formulation and touch briefly on some of the ideas around it as found in the texts.

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Title: Shortest length geodesics on closed hyperbolic surfaces
Speaker: Bidyut Sanki IISc
Date: 17 July 2014
Time: 10:00am - :11:00am
Venue: Lecture Hall III, Department of Mathematics

Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on the surface, in fact a so called fat graph, which we call the systolic graph. The central question that we study in this thesis is: which fat graphs are systolic graphs for some surface - we call such graphs admissible. This is motivated in part by the observation that we can naturally decompose the moduli space of hyperbolic surfaces based on the associated systolic graphs. A systolic graph has a metric on it, so that all cycles on the graph that correspond to geodesics are of the same length and all other cycles have length greater than these. This can be formulated as a simple condition in terms of equations and inequations for sums of lengths of edges. We call this combinatorial admissibility. Our first main result is that admissibility is equivalent to combinatorial admissibility. This is proved using properties of negative curvature, specifically that polygonal curves with long enough sides, in terms of a lower bound on the angles, are close to geodesics. Using the above result, it is easy to see that a subgraph of an admissible graph is admissible. Hence it suffices to characterize minimal non-admissible fat graphs. Another major result of this thesis is that there are infinitely many minimal non-admissible fat graphs (in contrast, for instance, to the classical result that there are only two minimal non-planar graphs).

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Title: Thurston-Teichmller theory and the dynamics of grafting
Speaker: Subhojoy Gupta Caltech
Date: 16 July 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall III, Department of Mathematics

Complex projective structures on a surface S arise in the complex-analytic description of Teichmller space. The operation of grafting parametrizes the space P(S) of such structures, and yields paths in Teichmller space called grafting rays. I shall introduce these, and describe a result concerning their asymptotic behavior. This talk shall be mostly expository.

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Title: An introduction to preferential attachment schemes
Speaker: Sunder Sethuraman University of Arizona
Date: 15 July 2014
Time: (1) 10:00 - 11:00 am (2) 2:00 - 3:00 pm
Venue: Lecture Hall III, Department of Mathematics

Informally, a preferential attachment scheme is a dynamic (reinforcement) process where a network is grown by attaching new vertices to old ones selected with probability proportional to their weight, a function of their degrees. In these two talks, we give an introduction to these schemes and discuss a couple of approaches to the study of the large scale degree structure of these graphs. One fruitful approach is to view the scheme in terms of branching processes. Another is to understand it in terms of Markov decompositions and fluid limits.

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Title: On shift-like automorphisms of C^k
Speaker: Sayani Bera IISc
Date: 15 July 2014
Time: 4:00 - 5:00pm
Venue: Lecture Hall III, Department of Mathematics

We will use transcendental shift-like automorphisms of C^k ,k>2 to construct two examples of non-degenerate entire mappings with prescribed ranges. The first example generalizes a result of Dixon-Esterle in C^2, i.e., we construct an entire mapping of C^k, k>2 whose range avoids a given polydisc but contains the complement of a slightly larger concentric polydisc. The second example shows the existence of a Fatou-Bieberbach domain in C^k, k>2 that is constrained to lie in a prescribed region. This is motivated by similar results of Buzzard and Rosay-Rudin.

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Title: A Posteriori Error Analysis of Discontinuous Galerkin Methods for Elliptic Variational Inequalities
Speaker: Ms. Kamana Porwal IISc
Date: 14 July 2014
Time: 11:00 a.m. - 12:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

Unlike the partial differential equations, the solutions of variational inequalities exhibit singularities even when the data is smooth due to the existence of free boundaries. Therefore the numerical procedure of these problems based on uniform refinement becomes inefficient due to the loss of the order of convergence. A popular remedy to enhance the efficiency of the numerical method is to use adaptive finite element methods based on computable a posteriori error bounds. Discontinuous Galerkin methods play a very important role in the local mesh adaptive refinement techniques.

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Title: Morse theory on the space of paths on Homogenous spaces
Speaker: Chaitanya Senapathi TIFR
Date: 11 July 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

1961 Frankel in a novel approach used the curvature of Complex Projective space to show complex submanifolds of complimentary dimension intersect. Based on this approach Scheon and Wolfson reproved the Barth-Lefshetz type theorems using the Morse Theory on the space of paths, in the case the ambient space is a Hermitian Symmetric Space. In this talk we describe how to extend their work to a much larger class of Homogenous spaces.

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Title: An Introduction to Minimal Surfaces
Speaker: Mr. Devang S Ram Mohan IISc
Date: 10 July 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall III, Department of Mathematics

In this presentation we briefly recall some results on harmonic maps. Subsequently, we introduce the concept of minimal surfaces. After exploring a few examples, we mathematically formulate Plateau’s problem regarding the existence of a soap film spanning each closed, simple wire frame and discuss a solution. In conclusion, certain partial results regarding the uniqueness of such a soap film are discussed.

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Title: Dynamics of Distal Group Actions
Speaker: Ridhdi Shah
Date: 25 June 2014
Time: 3-4 pm
Venue: LH 1

An automorphism T of a locally compact group is said to be distal if the closure of the T-orbit of any nontrivial element stays away from the identity. We discuss some properties of distal actions on groups. We will also relate distal groups with behaviour of powers of probability measures on it.

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Title: Dynamics of Distal Group Actions
Speaker: Dr. Ridhdi Shah
Date: 25 June 2014
Time: 3:00-4:00 p.m.
Venue: Lecture Hall 1, Department of Mathematics

An automorphism T of a locally compact group is said to be distal if the closure of the T-orbit of any nontrivial element stays away from the identity. We discuss some properties of distal actions on groups. We will also relate distal groups with behaviour of powers of probability measures on it.

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Title: Some Problems in Multivariable Operator Theory
Speaker: Mr. Santanu Sarkar (IISc)
Date: 23 June 2014
Time: 11.30 a.m.
Venue: Lecture Hall I, Department of Mathematics

This thesis investigates two different types of problems in multi variable operator theory. The first one deals with the defect sequence for contractive tuples and maximal contractive tuples. The second one deals with the wandering subspaces of the Bergman space and the Dirichilet space over polydisc. These are described in (I) and (II) below.

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Title: Analysis based fast algorithms for applied mathematics
Speaker: Prof. Sivaram Ambikasaran (Courant Institute of Mathematical Sciences, NYU)
Date: 12 June 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

The dominant problem in applied mathematics is the application of linear operators and solving linear equations. Dense linear systems arise in numerous applications: Boundary integral equations for elliptic partial differential equations, covariance matrices in statistics, Bayesian inversion, Kalman filtering, inverse problems, radial basis function interpolation, density functional theory, multi-frontal solvers for sparse linear systems, etc. As the problem size increases, large memory requirements scaling as $O(N^2)$ and extensive computational time to perform matrix algebra scaling as $O(N^2)$ or $O(N^3)$ make computations impractical, where $N$ is the underlying number of degrees of freedom. This talk will discuss new fast algorithms that scale as $O(N)$ for a class of problems, given a prescribed tolerance. Applications in the context of Gaussian processes, Integral equations for electromagnetic scattering, Symmetric factorization for Brownian dynamics, Bayesian inversion, Kalman filtering, multi-frontal solvers will also be presented.

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Title: Constant Mean Curvature surfaces
Speaker: Prof. Rukmini Dey (HRI)
Date: 05 June 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

In this expository talk, I will focus on CMC surfaces which are not minimal surfaces. I will talk about the link between CMC surfaces and integrable systems. I will then talk about how CMC surfaces fall out of a constrained optimization problem. I will give examples of rotational and helicoidal CMC surfaces and the isometry between them. If time permits I will talk about the classification of CMC surfaces, namely its Weirstrass representation.

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Title: A dynamic model of capital inflow and financial crisis in a two country and multi-country framework over infinite time horizon
Speaker: Gopal Basak (ISI, Kolkata)
Date: 02 June 2014
Time: 2:00-3:00 pm
Venue: LH-I, department of mathematics

We construct a model of capital inflow in a two and multi-country framework. A capital-scarce country, typically a developing country with a high return on capital borrows from a capital-rich country, typically a developed country to finance domestic investment. In the process both the countries gain, raising the world welfare. We formulate the problem in terms of utility maximization with respect to both develop and developing countries’ perspective over infinite time horizon and numerically solve for optimal interest rate, borrowing/lending amount, exchange rate using dynamic programming principle.

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Title: Geometric Quantization and Coherent States
Speaker: Prof. Rukmini Dey (HRI)
Date: 30 May 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

In this expository talk, I will first review prequantization of symplectic manifolds. I will then talk of polarizations and geometric quantization. I will then focus on geometric quantization of Kahler manifolds and the Rawnsley coherent states. If time permits I will talk of coadjoint orbits and coherent states.

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Title: Compactness theorem for the spaces of distance measure spaces and Riemann surface laminations.
Speaker: Mr. Divakaran D.
Date: 23 May 2014
Time: 11.00 a.m. - 12.00 noon
Venue: Lecture Hall I, Department of Mathematics

Gromov’s compactness theorem for metric spaces, a compactness theorem for the space of compact metric spaces equipped with the Gromov-Hausdorff distance, is a landmark theorem with many applications. We give a generalisation of this result - more precisely, we prove a compactness theorem for the space of distance measure spaces equipped with the generalised Gromov-Hausdorff-Levi-Prokhorov distance. A distance measure space is a triple (X, d, μ), where (X, d) forms a distance space (a generalisation of a metric space where, we allow the distance between two points to be infinity) and μ is a finite Borel measure.

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Title: Roots of Units, or A sum worthy of Gauss
Speaker: Chandan Singh Dalwat HRI
Date: 06 May 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

One looks at a certain sum G involving the p-th roots of unity (where p is a prime number), called the quadratic gaussian sum. It is easy to see that G^2=p, which means that G itself is either the positive or the negative square root of p. Which one ? It took Gauss many years to find the answer and to prove the result. Since then some other proofs of this result have been given, and it has become the central example of what is called the root number of an L-function. So the result is very important.

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Title: Contractivity and Complete contractivity
Speaker: Mr. Avijit Pal (IISc)
Date: 02 May 2014
Time: 2:00 - 3:00pm
Venue: Lecture Hall I, Department of Mathematics

We study homomorphisms $\rho_{V}$ given by $\rho_{V}(f)= \begin{pmatrix} f(w)I_n & \sum_{i=1}^{m} \partial_i f(w) V_{i} \\ 0 & f(w) I_n \end{pmatrix}$, $f \in \mathcal{O} (\Omega_{\mathbf{A}})$ defined on $\mathcal{O} (\Omega_{\mathbf{A}})$, where $\Omega_{\mathbf{A}}$ is a bounded domain of the form $\Omega_\mathbf A := \{ (z_1 ,z_2, \ldots, z_m) : | z_1 A_1 + \cdots + z_m A_m |_{\rm op} < 1 \}$ for some choice of a linearly independent set of $n\times n$ matrices $\{ A_1, \ldots, A_m \}.$

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Title: Cryptanalysis of RSA Variants and Implicit Factorization
Speaker: Santanu Sarkar CMI
Date: 01 May 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

The famous RSA public key cryptosystem is possibly the most studied topic in cryptology research. For efficiency and security purposes, some variants of the basic RSA has been proposed. In this talk, we will first discuss two such RSA variants: Prime Power RSA and Common Prime RSA.

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Title: Brownian excursions into an interval
Speaker: Navin Kashyap IISc, Bangalore
Date: 30 April 2014
Time: 2:00pm
Venue: LH-1, Department of Mathematics, IISc

The dynamics of excursions of Brownian motion into a set with more than one boundary point , which no longer have the structure of a Poisson process, requires an extension of Ito’s excursion theory , due to B.Maisonneuve. In this talk we provide a `bare hands’ calculation of the relevant objects - local time, excursion measure - in the simple case of Brownian excursions into an interval (a,b), without using the Maisonneuve theory. We apply these computations to calculate the asymptotic distribution of excursions into an interval, straddling a fixed time t, as t goes to infinity.

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Title: An Introduction to Minimal Surfaces
Speaker: Mr. Devang S Ram Mohan IISc
Date: 29 April 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

In this presentation we briefly recall some results on harmonic maps. Subsequently, we introduce the concept of minimal surfaces. After exploring a few examples, we mathematically formulate Plateau’s problem regarding the existence of a soap film spanning each closed, simple wire frame and discuss a solution. In conclusion, certain partial results regarding the uniqueness of such a soap film are discussed.

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Title: On Walkup's class of manifolds and tight triangulations
Speaker: Mr. NITIN SINGH
Date: 28 April 2014
Venue: Lecture Hall - I, Department of Mathematics, IISc

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Title: HOMOGENEOUS OPERATORS AND SOME IRREDUCIBLE REPRESENTATIONS OF THE MOBIUS GROUP
Speaker: Mr. Chandramouli. K IISc
Date: 28 April 2014
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

In this report, after recalling the definition of the M\\obius group, we define homogeneous operators, that is, operators $T$ with the property $\\varphi(T)$ is unitarily equivalent to $T$ for all $\\varphi$ in the M\\obius group and prove some properties of homogeneous operators. Following this, (i) we describe isometric operators which are homogeneous. (ii) we describe the homogeneous operators in the Cowen-Douglas class of rank 1. Finally, Multiplier representations which occur in the study of homogeneous operators are discussed. Following the proof of Kobayashi, the multiplier representations are shown to be irreducible.

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Title: Optimal Design Problems
Speaker: M. Vanninathan, TIFR-CAM
Date: 25 April 2014
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Motivated by applications,we introduce a class of optimization problems with constraints.Difficulties in solving these problems are highlighted.Mathematical developments to overcome these difficulties are discussed.

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Title: On the structure of proper holomorphic mappings
Speaker: Mr. Jaikrishnan Janardhanan IISc
Date: 11 April 2014
Time: 2:30 - 3:30pm
Venue: Lecture Hall I, Department of Mathematics

The aim of this thesis is to give explicit descriptions of the set of proper holomorphic mappings between two complex manifolds with reasonable restrictions on the domain and target spaces. Without any restrictions, this problem is intractable even when posed for domains in C^n. We present results for special classes of manifolds. We study, broadly, two types of structure results:

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Title: A Characterisation of the Fourier transform on the Heisenberg group
Speaker: Dr. Lakshmi Lavanya IISc
Date: 11 April 2014
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

A recent theorem of S. Alesker, S. Artstein-Avidan and V. Milman characterises the Fourier transform on R^n as essentially the only transform on the space of tempered distributions which interchanges convolutions and pointwise products. Analogously, we study the image of the Schwartz space on the Heisenberg group under the Fourier transform and obtain a similar characterisation for the Fourier transform on the Heisenberg group. This is a joint work with Prof. S. Thangavelu.

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Title: A Characterisation of the Fourier transform on the Heisenberg group
Speaker: Dr. Lakshmi IISc
Date: 11 April 2014
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

A recent theorem of S. Alesker, S. Artstein-Avidan and V. Milman characterises the Fourier transform on R^n as essentially the only transform on the space of tempered distributions which interchanges convolutions and pointwise products. Analogously, we study the image of the Schwartz space on the Heisenberg group under the Fourier transform and obtain a similar characterisation for the Fourier transform on the Heisenberg group. This is a joint work with Prof. S. Thangavelu.

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Title: A formal proof of Feit-Higman theorem in Agda
Speaker: Mr. Balaji Department of Mathematics.
Date: 07 April 2014
Time: 10.00 a.m.
Venue: Lecture Hall I, Department of Mathematics

Generalised polygons are incidence structures that generalise projective planes (generalised triangles) and are closely related to finite groups. The Feit-Higman theorem states that any generalised n-gon is either an ordinary polygon or n = 2, 3, 4, 6, 8 or 12.

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Title: Recent progress towards the twin prime conjecture
Speaker: Satadal Ganguly ISI Kolkata
Date: 28 March 2014
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

A great progress on the twin prime problem was made last year by Yitang Zhang and it made him famous in Mathematical circles almost overnight. He proved the existence of a positive real number M such that there are infinitely many pairs of primes that differ by at most M. The twin prime conjecture predicts that M can be taken to be two. I shall give an overview of the works leading up to Zhang’s spectacular achievement.

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Title: Quadrature domains - an introduction
Speaker: Kaushal Verma IISc
Date: 28 March 2014
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Quadrature domains are those on which holomorphic functions satisfy a generalized mean value equality. The purpose of this talk will be to reflect on the Schwarz reflection principle and to understand how it leads to examples of quadrature domains.

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Title: A Posteriori Error Analysis of Discontinuous Galerkin Methods for Elliptic Variational Inequalities
Speaker: Ms. Kamana Porwal IISc
Date: 25 March 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

Discontinuous Galerkin methods have received a lot of attention in the past two decades since these are high order accurate and stable methods which can easily handle complex geometries, irregular meshes with hanging nodes and different degree polynomial approximation in different elements. Adaptive algorithms refine the mesh locally in the region where the solution exhibits irregular behaviour and a posteriori error estimates are the main tools to steer the adaptive mesh refinement. In this talk, we present a posteriori error analysis of discontinuous Galerkin methods for variational inequalities of the first kind and the second kind. Particularly, we study the obstacle problem and the Signorini problem in the category of variational inequalities of the first kind and the plate frictional contact problem for the variational inequality of the second kind. Numerical examples will be presented to illustrate the theoretical results.

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Title: On the global character of the solutions of some nonlinear difference equations
Speaker: Esha Chatterjee Ghosh
Date: 21 March 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall III, Department of Mathematics

Non linear difference equations of order more than one is a relatively new and dynamic area of research in applied mathematics. In particular, the theory of Rational difference equations emerged in the last two decades and is an ongoing challenging field of study. In this talk we will present a brief introduction to nonlinear difference equations with some applications to various fields. Some techniques used in the qualitative analysis of the global character of solutions will be outlined. We will also discuss the results of a recent paper in which the speaker has addressed and generalized, an open problem posed by E. Camouzis and G. Ladas.

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Title: Critical Growth Elliptic Problem with Singular Discontinuous Nonlinearity in R^2
Speaker: Dr. Dhanya IISc
Date: 14 March 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

Elliptic problems with discontinuous nonlinearity has its own difficulties due to the non-differentiability of the associated functional. Hence, a generalized gradient approach developed by Chang has been used to solve such problems if the associated functional is known to be Lipchitz continuous. In this talk, we will consider critical elliptic problem in a bounded domain in $\\mathbb{R}^2$ with the simultaneous presence of a Heaviside type discontinuity and a power-law type singularity and investigate the existence of multiple positive solutions. Here discontinuity coupled with singularity does not fit into any of the known framework and we will discuss our approach employed to obtain positive solutions.

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Title: Discontinuous Galerkin Methods for Diffusion-Dominated Radiative Transfer Problems
Speaker: Prof. Dr. Guido Kanschat University of Heidelberg
Date: 11 March 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

While discontinuous Galerkin (DG) methods had been developed and analyzed in the 1970s and 80s with applications in radiative transfer and neutron transport in mind, it was pointed out later in the nuclear engineering community, that the upwind DG discretization by Reed and Hill may fail to produce physically relevant approximations, if the scattering mean free path length is smaller than the mesh size. Mathematical analysis reveals, that in this case, convergence is only achieved in a continuous subspace of the finite element space. Furthermore, if boundary conditions are not chosen isotropically, convergence can only be expected in relatively weak topology. While the latter result is a property of the transport model, asymptotic analysis reveals, that the forcing into a continuous subspace can be avoided. By choosing a weighted upwinding, the conditions on the diffusion limit can be weakened. It has been known for long time, that the so called diffusion limit of radiative transfer is the solution to a diffusion equation; it turns out, that by choosing the stabilization carefully, the DG method can yield either the LDG method or the method by Ern and Guermond in its diffusion limit. Finally, we will discuss an efficient and robust multigrid method for the resulting discrete problems.

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Title: A Posteriori Error Analysis of Discontinuous Galerkin Methods for Elliptic Variational Inequalities
Speaker: Ms. Kamana Porwal IISc
Date: 11 March 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

Discontinuous Galerkin methods have received a lot of attention in the past two decades since these are high order accurate and stable methods which can easily handle complex geometries, irregular meshes with hanging nodes and different degree polynomial approximation in different elements. Adaptive algorithms refine the mesh locally in the region where the solution exhibits irregular behaviour and a posteriori error estimates are the main tools to steer the adaptive mesh refinement. In this talk, we present a posteriori error analysis of discontinuous Galerkin methods for variational inequalities of the first kind and the second kind. Particularly, we study the obstacle problem and the Signorini problem in the category of variational inequalities of the first kind and the plate frictional contact problem for the variational inequality of the second kind. Numerical examples will be presented to illustrate the theoretical results.

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Title: On the Gromov hyperbolicity of convex domains
Speaker: Herve Gaussier Fourier Institut, Grenoble
Date: 10 March 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

We discuss the Gromov hyperbolicity of the Kobayashi metric on smooth convex domains in Euclidean space. We prove that if the boundary contains a holomorphic disc then the domain is not hyperbolic. On the other hand we give examples of convex (but not strongly pseudoconvex) domains which are hyperbolic. This is a joint work with Harish Seshadri.

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Title: On open three-manifolds
Speaker: Gerard Besson Fourier Institut, Grenoble
Date: 07 March 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

We will describe quite carefully two classes of open three-manifolds. For one of them almost nothing is known about its Riemannian geometry and we will state open questions. For the second class a theorem is available as well as a complete classification.

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Title: On the Gromov hyperbolicity of convex domains
Speaker: Herve Gaussier Fourier Institut, Grenoble
Date: 05 March 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

We discuss the Gromov hyperbolicity of the Kobayashi metric on smooth convex domains in Euclidean space. We prove that if the boundary contains a holomorphic disc then the domain is not hyperbolic. On the other hand we give examples of convex (but not strongly pseudoconvex) domains which are hyperbolic. This is a joint work with Harish Seshadri.

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Title: A series identity, possibly connected with a divisor problem, in Ramanujan's Lost Notebook
Speaker: Atul Dixit Tulane University
Date: 05 March 2014
Time: 5:00 - 6:00 p.m.
Venue: Lecture Hall II, Department of Mathematics

On page 336 in his lost notebook, S. Ramanujan proposes an identity that may have been devised to attack a divisor problem. Unfortunately, the identity is vitiated by a divergent series appearing in it. We prove here a corrected version of Ramanujan’s identity. While finding a plausible explanation for what may have led Ramanujan to consider a series that appears in this identity, we are led to a connection with a generalization of the famous summation formula of Vorono. One of the ramifications stemming from this work allows us to obtain a one-variable generalization of two double Bessel series identities of Ramanujan that were proved only recently. This is work in progress and is joint with Bruce C. Berndt, Arindam Roy and Alexandru Zaharescu.

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Title: Support data and Balmer spectrum
Speaker: Dr. Umesh Dubey IISc
Date: 21 February 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

Grothendieck and Verdier introduced the notion of triangulated category to extract homological informations. This structure appear in many branches of Mathematics. Balmer introduced the notion of spectrum of tensor triangulated category as classifying support data. This opens a way for geometric study of theses abstract categorical data. Balmer also defined the structure sheaf on this spectrum and as an application reconstructed large class of schemes from the category of perfect complexes associated with them. In this talk we’ll recall Balmer’s construction of spectrum and its application to reconstruction problem. We’ll also discuss computation of Balmer spectrum for some other tensor triangulated categories obtained in a joint work with Vivek Mallick.

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Title: How to integrate entire functions in polar coordinates?
Speaker: Dr. S. Thangavelu IISc
Date: 14 February 2014
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

In this talk we address the problem of integrating entire functions (of several complex variables) in ‘polar coordinates’!

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Title: Powers in products of terms of Pell's and Pell-Lucas Sequences
Speaker: Prof Shanta Laishram Indian Statistical Institute Delhi
Date: 12 February 2014
Time: 3:00 - 4:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

It is known that there are only finitely many perfect powers in non degenerate binary recurrence sequences. However explicitly finding them is an interesting and a difficult problem for binary recurrence sequences. A recent breakthrough result of Bugeaud, Mignotte and Siksek states that Fibonacci sequences (F_n) given by F_0 = 0; F_1 = 1 and F_{n+2} = F_{n+1} + F_n for n >= 0 are perfect powers only for F_0 = 0; F_1 = 1; F_2 = 1; F_6 = 8 and F_12 = 144.

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Title: On weak universality for directed polymers
Speaker: Prof Konstantin Khanin University of Toronto
Date: 10 February 2014
Time: 3:15 - 4:15 p.m.
Venue: Lecture Hall I, Department of Mathematics

The talk is based on a joint paper with T.Alberts and J.Quastel. We consider directed polymers in a random environment. However the inverse temperature is scaled with the length of a polymer. It turn out that with a proper critical scaling one can get a nontrivial universal behaviour for the partition function and the end point distribution. Moreover the limiting partition function distribution asymptotically converges to the Tracy-Widom law as the rescaled inverse temperature tends to infinity.

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Title: From random matrices to long range dependence
Speaker: Prof Arijit Chakrabarty ISI Delhi
Date: 10 February 2014
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this talk. It is shown that the limiting spectral distribution is determined by the absolutely continuous component of the spectral measure of the stationary process, a phenomenon resembling that in the situation where the entries of the matrix are i.i.d. On the other hand, the discrete component contributes to the limiting behavior of the eigenvalues in a completely different way. Therefore, this helps to define a boundary between short and long range dependence of a stationary Gaussian process in the context of random matrices.

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Title: Linear Algebra 1.5
Speaker: Prof. Dr. Martin Kreuzer University of Passau, Germany
Date: 07 February 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

Most algebraist believe they know Linear Algebra. The purpose of this talk is to indicate that this is not necessarily true. We show a substantial amount of little known basic Linear Algebra and its connection to Algebraic Geometry, in particular to the theory of zero-dimensional subschemes of affine spaces, and to Computer Algebra, in particular to the task of solving zero-dimensional polynomial systems. Here are some questions which we will answer in this talk: What are the big kernel and the small image of an endomorphism? What are its eigenspaces and generalized eigenspaces if it has no eigenvalues? What is the kernel of an ideal? What is a commendable endomorphism? And what is a commendable family of endomorphisms? How is this connected to curvilinear and Gorenstein schemes? And how can you use this to solve polynomial systems?

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Title: An algorithm for locating the nucleolus of assignment games.
Speaker: Prof T.E.S. Raghavan University of Illinois at Chicago
Date: 29 January 2014
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

In cooperative game theory , Shapley value and the nucleolus are two fundamental solution concepts. They associate a unique imputation for the players whose coalitional worths are given a priori.

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Title: Policy improvement algorithm for zero sum two person stochastic games of perfect information in Cesaro payoffs.
Speaker: Prof T.E.S. Raghavan University of Illinois at Chicago
Date: 28 January 2014
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

If the data defining a problem and at least one solution to the problem lie in the same Archimedean ordered field induced by the data, we say that the problem has order field property. When this property holds one may hope to do only finitely many arithmetic operations on the data to arrive at one such a solution. For example if we start with rational data, the value and a pair of optimal strategies for the players in a zero sum two person game have rational entries. This was first noticed by Herman Weyl , and it was a precursor to solving them via the simplex method. For bimatrix games while Nash exhibited an equilibrium in mixed strategies, it was Vorobev and Kuhn who checked that the order field property holds for bimatrix games. Later Lemke and Howson gave the so called linear complementarity algorithm to locate an equilibrium pair in the same data field. For three person games, Nash with Shapley constructed simple counter examples for lack of order field property. In general stochastic games fail to have order field property.

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Title: Constructions of Boolean Functions that are Significant in Cryptography and Coding Theory
Speaker: Prof Sumanta Sarkar ISI Kolkata
Date: 20 January 2014
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

A Boolean function is a mapping from the set of all binary n-tuples to the set {0, 1}. Boolean functions are important building blocks in designing secure cryptosystems known as stream ciphers. Boolean functions also form an important class of linear codes, known as the Reed-Muller codes. Over the last few decades, a lot of research has been done on Boolean function for its applications in cryptography and coding theory.

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Title: Approximation Theory and the Design of Fast Algorithms
Speaker: Dr. Nisheeth Vishnoi Microsoft Research, Bangalore
Date: 17 January 2014
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

I will talk about techniques to approximate real functions such as $x^s,$ $x^{-1}$ and $e^{-x}$ by simpler functions and how these results can be used in the design of fast algorithms. The key lies in the fact that such approximations imply faster ways to approximate primitives such as $A^sv,$ $A^{-1}v$ and $\\exp({-A})v$, and in the computation of matrix eigenvalues and eigenvectors. Indeed, many fast algorithms reduce to the computation of such primitives, which have proved useful for speeding up several fundamental computations, such as random walk simulation, graph partitioning, solving linear systems of equations, and combinatorial approaches for solving semi-definite programs.

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Title: Some Problems in Multivariable Operator Theory
Speaker: Mr. Santanu Sarkar (IISc)
Date: 13 January 2014
Time: 3:00 - 4:00pm
Venue: Lecture Hall I, Department of Mathematics

This thesis investigates two different types of problems in multi-variable operator theory. The first one deals with the defect sequence for a contractive tuple and the second one deals with wandering subspaces of the Bergman space and the Dirichlet space over the polydisc. These are described in (I) and (II) below.

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Title: L-4 norms of cusp forms in the level aspect
Speaker: Prof Rizwanur Khan Texas A&M university at Qatar
Date: 03 January 2014
Time: 3:00 - 4:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

Modular forms, particularly cusp forms, are ubiquitous objects in mathematics. A natural way to understand a cusp form is to study its L-p norms, for in principle the distribution of a function can be recovered from the knowledge of its moments. In this talk I will describe a new bound for the L-4 norm of a cusp form of prime level q, as q tends to infinity. This work is joint with Jack Buttcane.

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Title: On some generalizations and applications of Eisenstein-Dumas and Schonemann Criteria
Speaker: Prof Sudesh K. Khanduja IISER, Mohali
Date: 19 December 2013
Time: 11:30 - 12:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

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Title: Microlocal Analysis and Tomography
Speaker: Prof Todd Quinto Tufts University
Date: 12 December 2013
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall V, Second floor(new wing), Department of Mathematics

We consider the reconstruction problem for limited angle tomography using filtered backprojection (FBP). We introduce microlocal analysis and use it to explain why the well-known streak artifacts are present at the end of the limited angular range. We explain how to mitigate the streaks and prove that our modified FBP operator is a standard pseudodifferential operator, and so it does not add artifacts. We provide reconstructions to illustrate our mathematical results. This is joint work with Juergen Frikel, Helmholtz Zentrum, Muenchen.

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Title: On Frankl's conjecture
Speaker: Aniruddha Venkata Centre for Excellence in Basic Sciences, Mumbai
Date: 12 December 2013
Time: 2:00 - 3:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

A family of sets is said to be union-closed if the union of any two sets from the family remains in the family. Frankl’s conjecture, aka the union-closed sets conjecture, is the remarkable statement that for any finite union-closed family of finite sets, there exists an element that belongs to at least half of the sets in the family. Originally stated in 1979, it is still wide open. This will be an informal discussion on progress towards the conjecture.

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Title: On the structure of proper holomorphic mappings
Speaker: Mr. Jaikrishnan Janardhanan IISc
Date: 11 December 2013
Time: 11.00 am - 12.00 noon
Venue: Lecture Hall I, Department of Mathematics

The aim of this thesis is to give explicit descriptions of the set of proper holomorphic mappings between two complex manifolds with reasonable restrictions on the domain and target spaces. Without any restrictions, this problem is intractable even when posed for domains in C^n. We present results for special classes of manifolds. We study, broadly, two types of structure results:

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Title: Low dimensional projective groups
Speaker: Prof Mahan Mj RKM Vivekananda University
Date: 10 December 2013
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

Fundamental groups of smooth projective varieties are called projective groups. We shall discuss (cohomological) conditions on dimension that force such a group to be the fundamental group of a Riemann surface.

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Title: New directions in complex analysis on symmetric domain
Speaker: Professor Harald Upmeier University of Marburg, Germany
Date: 04 December 2013
Venue: LH-I, department of Mathematics.

The Lectures will focus on topics that go beyond the classical framework of Hilbert spaces of holomorphic functions (Bergman spaces, Hardy spaces) on the unit ball or more general bounded symmetric domains. The main point is to include vector-valued functions and even cohomology classes for non-convex domains. The plan of the lectures is as follows:

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Title: Preserving positivity for rank-constrained matrices
Speaker: Prof Apoorva Khare Stanford university
Date: 28 November 2013
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

We study the problem of characterizing functions, which when applied entrywise, preserve Loewner positivity on distinguished submanifolds of the cone of positive semidefinite matrices. Following the work of Schoenberg and Rudin (and several others), it is well-known that entrywise functions preserving positivity in all dimensions are necessarily absolutely monotonic. However, there are strong theoretical and practical motivations to study functions preserving positivity in a fixed dimension $n$. Such characterizations are known only in the $n=2$ case.

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Title: Incidence geometries and Algebraic Codes
Speaker: Prof N.S. Narasimha Sastry ISI Bangalore
Date: 22 November 2013
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

Tits theory of spherical buildings gives a uniform geometric context to study all finite simple groups (except the alternating groups and the sporadic simple groups) and simple algebraic groups. More generally, the theory of buildings is central to the Lie theory associated with infinite root systems. These structures are `built of’ two basic objects: Coxeter complexes and Moufang generalized polygons. The generalized polygons (which includes projective planes) are rank 2 geometries (incidence geometries with 2 kind of objects - points and lines - and an incidence relation among them) whose classification is fundament, difficult and perhaps impossible.

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Title: Incidence geometries and Algebraic Codes
Speaker: Prof N.S. Narasimha Sastry ISI Bangalore
Date: 15 November 2013
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

Tits theory of spherical buildings gives a uniform geometric context to study all finite simple groups (except the alternating groups and the sporadic simple groups) and simple algebraic groups. More generally, the theory of buildings is central to the Lie theory associated with infinite root systems. These structures are `built of’ two basic objects: Coxeter complexes and Moufang generalized polygons. The generalized polygons (which includes projective planes) are rank 2 geometries (incidence geometries with 2 kind of objects - points and lines - and an incidence relation among them) whose classification is fundament, difficult and perhaps impossible.

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Title: Admission Prices and Welfare in Queues
Speaker: D. Manjunath (IIT, Bombay)
Date: 11 November 2013
Time: 2:00pm
Venue: LH-II, Department of Mathematics, IISc

A multiqueue system serves a multiclass population. Classes differ in their valuation of time. Oblivious routing in which routing is not informed by current queue status or past decisions is assumed. First, we explore the structure of the routing fractions that maximise social welfare. We then analyse the case customer are strategic and the queues have an admission price. We then argue that admission prices can be set to achieve optimal routing.

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Title: On Abhyankar's inertia conjecture
Speaker: Prof Manish Kumar ISI Bangalore
Date: 08 November 2013
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

The conjecture is about various subgroup that can occur as the inertia subgroup of an etale Galois cover of an affine line at a point above infinity over an algebraically closed field of positive characteristic. I will explain this conjecture and mention some positive results supporting this conjecture.

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Title: Beurling-Lax-Halmos Theorem and Operator Theory
Speaker: Prof Jaydeb Sarkar, ISI Bangalore
Date: 25 October 2013
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

This talk will be an elementary introduction to (Hilbert) module approach to operator theory. We explore the relationship of the classical von Neumann-Wold decomposition theorem and the Beurling-Lax-Halmos theorem for isometries. We will also discuss a unified approach to the invariant subspace problem for bounded linear operators on Hilbert spaces. The talk will be accessible to general audience including graduate students.

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Title: Beurling-Lax-Halmos Theorem and Operator Theory
Speaker: Prof Jaydeb Sarkar ISI Bangalore
Date: 25 October 2013
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

This talk will be an elementary introduction to (Hilbert) module approach to operator theory. We explore the relationship of the classical von Neumann-Wold decomposition theorem and the Beurling-Lax-Halmos theorem for isometries. We will also discuss a unified approach to the invariant subspace problem for bounded linear operators on Hilbert spaces. The talk will be accessible to a general audience including graduate students.

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Title: Homotopy type and volume of locally symmetric spaces
Speaker: Prof C S Aravinda TIFR CAM Bangalore
Date: 23 October 2013
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

A conjecture of Gelander states that there is an effective triangulation in a compact deformation retract of a given locally symmetric space, giving linear bounds on the full homotopy type. This talk will explain some of this construction.

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Title: Homotopy type and volume of locally symmetric spaces
Speaker: Prof C S Aravinda TIFR Bangalore
Date: 23 October 2013
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics

A conjecture of Gelander states that there is an effective triangulation in a compact deformation retract of a given locally symmetric space, giving linear bounds on the full homotopy type. This talk will explain some of this construction.

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Title: Ramanujan and hypergeometric series
Speaker: Dr.K. Srinivasa Rao, FNASc.,FTNASc., Senior Professor (Retd.), IMSc
Date: 12 September 2013
Time: 3:00 - 4:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

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Title: Introduction to the mean curvature flow
Speaker: Dr. Franck Djiideme University of Benin
Date: 11 September 2013
Time: 3.30 p.m.
Venue: Lecture Hall III, Department of Mathematics

The mean curvature flow is a process under which a submanifold is deformed in its mean curvature vector’s direction. This process received more attention since it is an efficient way to construct submanifold which minimizes the volume : it is the negative gradient flow of volume functional. In this firs talk. I will discuss about basic tools in the study of mean curvature and describe some examples .

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Title: Discrete holomorphicity and quantized affine algebras
Speaker: Paul ZINN-JUSTIN Universite Pierre et Marie-Curie (Paris 6)
Date: 10 September 2013
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

We consider non-local currents in the context of quantized affine algebras. In two special cases, these currents can be identified with configurations in the six-vertex and Izergin–Korepin nineteen-vertex models. Mapping these to their corresponding Temperley–Lieb loop models, we directly identify non-local currents with discretely holomorphic loop observables. In particular, we show that the bulk discrete holomorphicity relation and its recently derived boundary analogue are equivalent to conservation laws for non-local currents. Joint with Y. Ikhlef, R. Weston and M. Wheeler.

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Title: Descent and Cohomological Descent
Speaker: Prof Nitin Nitsure, TIFR, Mumbai
Date: 26 August 2013
Time: 3:00 - 4:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Around 1960, Grothendieck developed the theory of descent. The aim of this theory is to construct geometric objects on a base space – in particular bundles, sheaves and their sections – in terms a generalized covering space which is visualized to lie upstairs' over the base space. The objects over the base space are obtained by descending’ similar objects from the covering space. In late 1960s-early 1970s, Deligne addressed the problem of how to understand cohomology of the base space via cohomology of a covering, by this time descending cohomology classes (instead of just descending global sections of sheaves, which is the case of 0th cohomology). The theory developed by Deligne, known as `Cohomological Descent’ has found important applications to Hodge theory and to cohomology of algebraic stacks. In these two expository lectures, I will begin with a quick look at Grothendieck’s theory of descent, and then go on to give a brief introduction to Deligne’s theory of Cohomological Descent.

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Title: Descent and Cohomological Descent
Speaker: Prof Nitin Nitsure, TIFR, Mumbai
Date: 23 August 2013
Time: 3:00 - 4:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Around 1960, Grothendieck developed the theory of descent. The aim of this theory is to construct geometric objects on a base space – in particular bundles, sheaves and their sections – in terms a generalized covering space which is visualized to lie upstairs' over the base space. The objects over the base space are obtained by descending’ similar objects from the covering space. In late 1960s-early 1970s, Deligne addressed the problem of how to understand cohomology of the base space via cohomology of a covering, by this time descending cohomology classes (instead of just descending global sections of sheaves, which is the case of 0th cohomology). The theory developed by Deligne, known as `Cohomological Descent’ has found important applications to Hodge theory and to cohomology of algebraic stacks. In these two expository lectures, I will begin with a quick look at Grothendieck’s theory of descent, and then go on to give a brief introduction to Deligne’s theory of Cohomological Descent.

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Title: Mixed Characteristic Polynomials and the Kadison-Singer Problem
Speaker: Prof Nikhil Srivastava Microsoft research, India
Date: 23 August 2013
Time: 2:00 - 4:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

The Kadison-Singer problem is a question in operator theory which arose in 1959 while trying to make Dirac’s axioms for quantum mechanics mathematically rigorous. Over the course of several decades, this question was reduced to several equivalent conjectures about finite matrices, and shown to have significant implications in applied mathematics, computer science, and various branches of pure mathematics.

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Title: Projective Normality of G.I.T. quotient varieties modulo finite solvable groups and Weyl groups
Speaker: Prof Santosh Pattanayak, Weizmann Inst. of Science, Israel
Date: 21 August 2013
Time: 3:00 - 4:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

We prove that for any finite dimensional vector space $V$ over an algebraically closed field $K$, and for any finite subgroup $G$ of $GL(V)$ which is either solvable or is generated by pseudo reflections such that the order $|G|$ is a unit in $K$, the projective variety $\mathbb P(V)/G$ is projectively normal with respect to the descent of $\mathcal{O}(1)^{\otimes |G|}$, where $\mathcal{O}(1)$ denotes the ample generator of the Picard group of $\mathbb P(V)$. We also prove that for the standard representation $V$ of the Weyl group $W$ of a semi-simple algebraic group of type $A_n , B_n , C_n , D_n , F_4$ and $G_2$ over $\mathbb{C}$, the projective variety $\mathbb P(V^m)/W$ is projectively normal with respect to the descent of $\mathcal{O}(1)^{\otimes |W|}$, where $V^m$ denote the direct sum of $m$ copies of $V.$

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Title: Nonlinear Schrodinger equation and the twisted Laplacian
Speaker: Dr. Vijay Kumar Sohani IISc, Bangalore
Date: 16 August 2013
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

In this lecture we will study the well posedness problem for the nonlinear Schr\\{o}dinger equation for the magnetic Laplacian on $\\R^{2n}$, corresponding to constant magnetic field, namely the twisted Laplacian on $\\C^n$. We establish the well posednes in certain first order Sobolev spaces associated to the twisted Laplacian, and also in $L^2(\\C^n)$.

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Title: Needles, bushes, hairbrushes and polynomials
Speaker: Prof Malabika Pramanik UBC, Canada
Date: 14 August 2013
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Points, lines and circles are among the most primitive and fundamental of mathematical concepts, yet few geometric objects have generated more beautiful and nontrivial mathematics. Deceptively simple in their formulation, many classical problems involving sets of lines or circles remain open to this day. I will begin with a sample that has spearheaded much of modern research, and explore connections with analysis, geometry, combinatorics - maybe also parallel parking.

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Title: Control of a queuing system under the moderate deviation scaling
Speaker: Prof. Anup Biswas Technion, Israel
Date: 12 August 2013
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

In recent times, exponential type cost structure has become popular in control theory. In this talk we formulate and discuss a risk- sensitive type control problem for a multi-class queuing system under the moderate deviation scaling. It is known that the rate function corresponding to the moderate deviation scaling is of Gaussian type. This property of the rate function is often useful for mathematical analysis. We show that the limiting game corresponding to our control problem is solvable. Also the limiting game has a similarity to the well-studied Brownian control problems. This problem is also related to a conjecture of Damon Wischik (2001). The main difficulty in working with G/G/1 queuing network is that the underlying state dynamics is not Markov. Markov property has proven useful for these type of problems (see e.g., Atar-Goswami-Shwartz(2012)). The standard way to solve these problems is to look at the pde associated with the state dynamics and sandwich the limiting value between the upper and lower value of the game. This technique does not work when the state dynamics is not Markov. We will see that the special structure of the rate function and moderate deviation settings will be helpful to overcome such difficulties. Extension to many-server models will also be discussed.

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Title: Weak solutions and convergence analysis of numerical methods for coagulation-fragmentation equations
Speaker: Prof. Ankik Kumar Giri Radon Inst. for Computational and Applied Mathematics (RICAM), Austria
Date: 07 August 2013
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

In this talk I will mainly focus on the existence and uniqueness of weak solutions to the nonlinear continuous coagulation and multiple fragmentation equations. In addition, the convergence analysis of two numerical methods (the fixed pivot technique and the cell average technique) for solving nonlinear coagulation or Smoluchowski equation is introduced. At the end, the convergence rates obtained from both the techniques are compared and mathematical results of the convergence analysis are also demonstrated numerically.

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Title: Gap Distributions and Homogeneous Dynamics
Speaker: Prof. Jayadev Athreya University of Illiniois, Urbana-Champaign
Date: 05 August 2013
Time: 3:30- 4:30pm
Venue: Department of Mathematics, LH-I

We discuss the notion of gap distributions of various lists of numbers in [0, 1], in particular focusing on those which are associated to certain low-dimensional dynamical systems. We show how to explicitly compute some examples using techniques of homogeneous dynamics. This works gives some possible notions of `randomness’ of special trajectories of billiards in polygons, and is based partly on joint works with J. Chaika, J. Chaika and S. Leliever, and with Y.Cheung.

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Title: The Hopf map, higher linking and friends
Speaker: Prof. Siddhartha Gadgil IISc
Date: 18 July 2013
Time: 3:00 - 4:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

Basic Algebraic Topology is built on considering objects (such as differential forms) up to boundary (e.g., exterior derivative). However, there is more structure in chains and boundaries that can be extracted by not immediately passing to quotients. We will discuss elementary examples of this, such as the Hopf invariant and Milnor’s higher linking.

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Title: Potential theory on infinite graphs
Speaker: Prof. Victor Anandam IMSc, Chennai
Date: 12 July 2013
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

The classical (as well as axiomatic) potential theory has been developed in the context of the study of analytic functions on Riemann surfaces, Newton potentials and Markov processes. This talk aims to develop a discrete version of potential theory on infinite graphs, based on the examples of electrical networks and infinite graphs.

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Title: A-infinity algebras and the homotopy transfer theorem II
Speaker: Dr. Micah Miller, IISc
Date: 10 July 2013
Time: 3:00 - 4:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

We will continue our discussion of the Homotopy Transfer Theorem for A-infinity algebras. We will introduce the notion of a minimal model for a dg algebra. This will allow us to relate quasi-isomorphisms between strict dg algebras and quasi-isomorphisms between A-infinity algebras.

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Title: Induction, equality, spaces, types, A_infinity: An introduction to HoTT
Speaker: Prof. Siddhartha Gadgil
Date: 08 July 2013
Time: 3:00 - 4:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

Homotopy Type Theory (HoTT), developed recently in a large collaboration centered at IAS, Princeton, combines elements from type theory, logic and topology to give alternative foundations of mathematics which are much closer to mathematical practice (useful for Automated Reasoning). HoTT also gives new insights into topology.

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Title: Induction, equality, spaces, types, A_infinity: An introduction to HoTT
Speaker: Prof. Siddhartha Gadgil IISc
Date: 08 July 2013
Time: 3:00 - 4:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

Homotopy Type Theory (HoTT), developed recently in a large collaboration centered at IAS, Princeton, combines elements from type theory, logic and topology to give alternative foundations of mathematics which are much closer to mathematical practice (useful for Automated Reasoning). HoTT also gives new insights into topology.

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Title: A-infinity algebras and the homotopy transfer theorem
Speaker: Dr. Micah Miller IISc
Date: 04 July 2013
Time: 3:00 - 4:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

We will introduce the notion of a differential graded algebra that is not strictly associative, but associative up to chain homotopy. Such objects are called A-infinity algebras or strong homotopy associative algebras. The goal is to state and prove the Homotopy Transfer Theorem, which states that any chain complex that is chain homotopic to an A-infinity algebra has an A-infinity structure and the maps in the chain homotopy can be lifted to a map of A-infinity algebras.

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Title: The Euler characteristic, projective modules and the Gersten-Witt complex
Speaker: Prof. Sarang Sane University of Kansas
Date: 02 July 2013
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

Starting with the Euler characteristic in graph theory/combinatorics, we trace a brief history, first viewing it as an Euler class in topology, then as an obstruction to splitting of vector bundles and finally get to the more recent notion of the Euler class in algebra/geometry and its use as an obstruction to the splitting of projective modules. This recent notion has two approaches, Euler class groups and Chow-Witt groups, the second of which uses the Gersten-Witt complex as mentioned in the title. Time permitting, we hope to state results about both approaches.

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Title: Glimpses of HOTT; Logic and Topology make elegant and useful Foundations
Speaker: Prof. Siddhartha Gadgil Indian Institute of Science
Date: 01 July 2013
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall III, Department of Mathematics

HOTT (homotopy type theory) is logic built on type theory (mostly from Computer Science) and ideas from topology to give foundations of mathematics that are very elegant and much closer to mathematical practice. This makes HOTT very useful for computer proof systems, and also gives a very nice new synthetic treatment of homotopy theory.

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Title: Glimpses of HOTT; Logic and Topology make elegant and useful Foundations
Speaker: Prof. Siddhartha Gadgil Indian Institute of Science
Date: 26 June 2013
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall III, Department of Mathematics

HOTT (homotopy type theory) is logic built on type theory (mostly from Computer Science) and ideas from topology to give foundations of mathematics that are very elegant and much closer to mathematical practice. This makes HOTT very useful for computer proof systems, and also gives a very nice new synthetic treatment of homotopy theory.

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Title: Generalized Radon transforms in image reconstruction problems
Speaker: Prof. Gaik Ambartsoumian University of Texas at Arlington
Date: 20 June 2013
Time: 4:00 - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Integral geometry is a field of mathematics that studies inversions and various properties of transforms, which integrate functions along curves, surfaces and hypersurfaces. Such transforms arise naturally in numerous problems of medical imaging, remote sensing, and non-destructive testing. The most typical examples include the Radon transform and its generalizations. The talk will discuss some problems and recent results related to generalized Radon transforms, and their applications to various problems of tomography.

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Title:
Speaker: Prof. Siddhartha Gadgil
Date: 11 June 2013
Venue: Lecture Hall III, Department of Mathematics

The informal seminar on mathematical reasoning continues. This meetingwill be self-contained (i.e., not dependent on previous sessions).

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Title: Preserving physical quantities of interest in finite elements with rational bubbles
Speaker: Prof. Johnny Guzman Division of Applied Mathematics, Borwn University, Providence.
Date: 22 May 2013
Time: 4.00pm - 5.00pm
Venue: Department of Mathematics, LH-1

Many commonly used mixed finite elements for the Stokes problem only conserve mass approximately. We show that if we supplement polynomial basis functions with divergence free rational functions in the finite element method we can conserve mass exactly. Similarly, we show how to supplement polynomial basis in the finite element space with rational functions in when approximating linear elasticity problems in order to preserve angular momentum exactly. This is joint work with Michael Neilan (University of Pittsburgh).

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Title: Gradient bounds for p-harmonic systems with vanishing Neumann data in a convex domain
Speaker: Agnid Banerjee, Purdue University
Date: 20 May 2013
Time: 11am
Venue: Department of Mathematics, LH-3

Let u be a weak solution to a p-harmonic system with vanishing Neumann data on a portion of the boundary of a domain which is convex. We show that subsolution type arguments for some uniformly elliptic PDE’s can be used to deduce that the modulus of the gradient is bounded depending on the Lipschitz character of the domain. In this context, I would like to mention that classical results on the boundedness of the gradient require the domain to be C^{1, Dini}. However, in our case, since the domain is convex, one can make use of the fundamental inequality of Grisvard which can be thought of as an analogue of the use of the barriers for Dirichlet problems in convex domains. Our arguments replaces an argument based on level sets in recent important works of Mazya, Cianchi-Mazya and Geng-Shen involving similar problems. I also intend to indicate some open problems in the regularity theory of degenerate elliptic and parabolic systems. This is a joint work with Prof. John L. Lewis.

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Title: Renormalization and reverse renormalization in the dynamics of germs of holomorphic diffeomorphisms in C.
Speaker: Kingshook Biswas Vivekananda University
Date: 17 May 2013
Time: 11-12 am.

We discuss the renormalization and reverse renormalization constructions used in studying the dynamics of germs of holomorphic diffeomorphisms fixing the origin in C with linear part a rotation. Such a germ is said to be linearizable if it is analytically conjugate to its linear part.

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Title: Moebius and conformal maps between boundaries of CAT(-1) spaces.
Speaker: Kingshook Biswas Vivekananda University
Date: 16 May 2013
Time: 11-12 am.

Motivated by rigidity problems for negatively curved manifolds, we study Moebius and conformal maps $f : \\partial X \\to \\partial Y$ between boundaries of CAT(-1) spaces $X, Y$ equipped with visual metrics.

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Title: A new class of high order finite volume schemes
Speaker: Prof. Philip Roe University of Michigan
Date: 13 May 2013
Time: 4:00 pm- 5:00pm
Venue: Department of Mathematics, LH-I

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Title: Geometrical treatment of geometric shock waves
Speaker: Prof. Philip Roe University of Michigan
Date: 10 May 2013
Time: 4:00 pm- 5:00pm
Venue: Department of Mathematics, LH-I

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Title: Differential Modular forms on Shimura curves over totally real fields
Speaker: Prof. Debargha Benerjee Australian National University
Date: 02 May 2013
Time: 4:00 pm- 5:00pm
Venue: Department of Mathematics, LH-III

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Title: Systolic inequalities
Speaker: Dr. Thomas Richard, IISc, Bangalore
Date: 16 April 2013
Time: 11: 30 a.m.
Venue: LH- II, Department of Mathematics

The systole of a compact Riemannian manifold (M,g) is the length of the shortest non contractible loop of M, it is attained by a periodic geodesic. A systolic inequality is a lower on the volume of any Riemannian metric depending only on the systole. If one consider the systole as a kind of ‘belt size’ of (M,g), a systolic inequality just says ‘the bigger the belt, the bigger the guy’. In this talk, we will discuss systolic inequalities for surfaces. We will prove optimal results for the torus and the projective plane (which go back to Loewner and Pu in the 50’s) and non optimal results for higher genus surfaces (due to Hebda and Gromov in the 80’s). This topic involve a nice mixture of metric geometry and elementary topology. If time permits, we will say a few words about higher dimensions.

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Title: Littlewood-Offord problem
Speaker: Prof. Manjunath Krishnapur IISc, Bangalore
Date: 05 April 2013
Time: 2:00-3:30 pm
Venue: Department of Mathematics, LH-1

In the seqries of 4 lectures, we will cover some aspects of the Littlewood-Offord problem. This problem concerns the anti-concentration phenomenon of sums of independent random variables and has applications to invertibility of random matrices and statistics of real zeros of random polynomials. The subject overlaps probability, combinatorics, additive combinatorics and some algebra.

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Title: Metric Measure spaces and Random matrices
Speaker: Prof. Siddhartha Gadgil, IISc, Bangalore
Date: 02 April 2013
Time: 11: 30 a.m.
Venue: LH- II, Department of Mathematics

The geometry of Metric spaces equipped with a probability measure is a very dynamic field. One motivation for the study of such spaces is that they are the natural limits of Riemannian manifolds in many contexts. In this talk, I will introduce basic properties of metric measure spaces and the Gromov-Prohorov distance on them. I will also discuss joint work with Manjunath Krishnapur in which we show that independently sampling points according to the given measure gives an asymptotically bi-Lipschitz correspondence between Metric measure spaces and Random matrices. Finally, I will briefly discuss work with Divakaran in which we study the compactification of the Moduli space of Riemann surfaces in terms of metric measure spaces.

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Title: Single and Multi-player Stochastic Dynamic Optimization.
Speaker: Subhamay Saha, IISc, Bangalore
Date: 01 April 2013
Time: 4:00 pm
Venue: Department of Mathematics, LH-1

In this thesis we investigate single and multi-player stochastic dynamic optimization problems in both discrete and continuous time. In the multi-player setup we investigate zero-sum games with both complete and partial information. We study partially observable stochastic games with average cost criterion and the state process being discrete time controlled Markov chain. We establish the existence of the value of the game and also obtain optimal strategies for both players. We also study a continuous time zero-sum stochastic game with complete observation. In this case the state is a pure jump Markov process. We investigate the finite horizon total cost criterion. We characterise the value function via appropriate Isaacs equations. This also yields optimal Markov strategies for both players.

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Title: On an ODE related to the Ricci flow
Speaker: Atreyee Bhattacharya IISc, Bangalore
Date: 28 March 2013
Time: 4:00 pm- 5:00 pm
Venue: Department of Mathematics, LH-III

We discuss two topics in this talk. First we study compact Ricci-flat 4- manifolds without boundary and obtain pointwise restrictions on curvature (not involving global quantities such as volume and diameter) which force the metric to be flat. We obtain the same conclusion for compact Ricci-flat Khler surfaces with similar but weaker restrictions on holomorphic sectional curvature. Next we study the reaction ODE associated to the evolution of the Riemann curvature operator along the Ricci flow. We analyze the behavior of this ODE near algebraic curvature operators of certain special type that includes the Riemann curvature operators of various symmetric spaces. We explicitly show the existence of some solution curves to the ODE connecting the curvature operators of certain symmetric spaces. Although the results of these two themes are different, the underlying common feature is the reaction ODE which plays an important role in both.

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Title: An exposition of selected tools from additive combinatorics
Speaker: Mokshay Madiman (Yale university)
Date: 08 March 2013
Time: 2:00-3:30 pm
Venue: LH-1, Department of mathematics.

Tools from additive combinatorics are finding their way into numerous areas of mathematics and applied mathematics, and in particular have been central to recent developments in both random matrix theory and harmonic analysis. The goal of this short course is to understand some of these tools. (If time permits and the audience is willing to pitch in with some talks, we may also cover selected applications.)

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Title: Geometrical shock dynamics and Shock vortex interaction
Speaker: Dr. Prasanna Varadarajan Schlumberger Gould Research, Cambridge
Date: 21 February 2013
Time: 4:00 pm-5:00 pm
Venue: LH-III, Department of Mathematics

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Title: Languages and Generalized Code Chains.
Speaker: Prof. R. D. Giri, Nagpur University.
Date: 20 February 2013
Time: 3:00 pm-4:00 pm
Venue: LH-III, Department of Mathematics

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Title: On condition numbers of a basis
Speaker: Professor B. V. Limaye (IIT Bombay)
Date: 19 February 2013
Time: 11:30 am-12:30 pm
Venue: LH-II, Department of Mathematics

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Title: Solutions for differential equations in fluid mechanics by different techniques
Speaker: Prof. Dinesh P. A. M. S. Ramaiah Institute of Technology
Date: 15 February 2013
Time: 4:00 pm- 5:00pm
Venue: Department of Mathematics, LH-I

Any real physical problem arising in fluid mechanics, when it is translated to mathematical approach generally govern a differential equation with some assumptions. The solution for such a study of the system is solved using analytical or numerical techniques. An attempt has been made to understand the characteristics or behavior or analysis of the physical system using different methods like Lighthills method, perturbation methods, rational approximation or Pad approximation, shooting technique and also highlights on the advantages and limitations of each method are discussed.

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Title: Normal spectrum of a subnormal operator
Speaker: Mr. Sumit Kumar IISc, Bangalore
Date: 15 February 2013
Time: 3-4pm
Venue: Department of Mathematics, Lecture Hall II

Let ${H}$ be a separable Hilbert space over the complex field. The class $S := \lbrace N|_{M} : N$ is normal on ${H}$ and ${M}$ is an invariant subspace for $N \rbrace$ of operators was introduced by Halmos and consists of subnormal operators. Each subnormal operator possesses a unique minimal normal extension $\hat{N}$ as shown by Halmos. Halmos proved that $\sigma(\hat{N}) \subseteq \sigma(S)$ and then Bram proved that $\sigma(S)$ is obtained by filling certain number of holes in the spectrum $\sigma(\hat{N})$ of the minimal normal extension $\hat{N}$ of a subnormal operator in ${S}$.

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Title: Surface diagrams and 4-manifolds (following Jonathan Williams)
Speaker: Siddhartha Gadgil
Date: 12 February 2013
Time: 11:15 a.m.
Venue: LH-III, Department of Mathematics

I will describe work of Jonathan Williams giving a description of smooth 4-manifolds in terms of certain collections of closed curves on surfaces and certain moves on them. This builds on constructions using Lefschetz pencils and their variants, but is a completely elementary description.

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Title: About the density of states in Random Operators
Speaker: Prof Krishna Maddaly IMSc, Chennai
Date: 12 February 2013
Time: 3:15 pm- 4:15 pm
Venue: Department of Mathematics, LH-III

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Title: Switching in biological networks
Speaker: Prof. Badal Joshi University of Minnesota
Date: 11 February 2013
Time: 4:00 pm- 5:00pm
Venue: Department of Mathematics, LH-I

(Bio)chemical reaction networks are used in systems biology to model gene regulatory, protein, metabolic, and other cellular networks. Since existence of multiple steady states (MSS) provides the underpinnings for switching in chemical reaction networks, it is a fundamental problem to determine which network structures permit MSS. There exist several criteria which, when satisfied, establish that a network does not permit MSS regardless of the parameter values. On the other hand, results that establish that a network does permit MSS are rare. I will describe our recent work which provides a novel approach towards solving this problem. In the second part of the talk, I will describe stochastic switching which occurs in a network of neurons which is responsible for the distinct brain states of sleep and wake and for the transitions between the two states.

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Title: Derived Geometry and Topological String Theory
Speaker: Dr. Pranav Pandit, University of Vienna
Date: 07 February 2013
Time: 3:30 p.m.
Venue: LH-III, Department of Mathematics

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Title: Switching in biological networks
Speaker: Prof. Badal Joshi University of Minnesota
Date: 06 February 2013
Time: 4:00 pm- 5:00pm
Venue: Department of Mathematics, LH-I

(Bio)chemical reaction networks are used in systems biology to model gene regulatory, protein, metabolic, and other cellular networks. Since existence of multiple steady states (MSS) provides the underpinnings for switching in chemical reaction networks, it is a fundamental problem to determine which network structures permit MSS. There exist several criteria which, when satisfied, establish that a network does not permit MSS regardless of the parameter values. On the other hand, results that establish that a network does permit MSS are rare. I will describe our recent work which provides a novel approach towards solving this problem. In the second part of the talk, I will describe stochastic switching which occurs in a network of neurons which is responsible for the distinct brain states of sleep and wake and for the transitions between the two states.

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Title: Real analytic maps and stable Hamiltonian structures
Speaker: Prof Ferit ztrk (Bogazii University, Turkey)
Date: 28 January 2013
Time: 3:30-4:30 pm
Venue: LH-I, Department of Mathematics

We consider a real analytic map f from R^4 to R^2 with a singularity at 0. One method to investigate the singularity is to work on its link L. If 0 is an isolated singularity then it is well known that L is a fibered link in the 3-sphere S^3. This describes immediately a contact structure on S^3. In this talk we suggest that even if 0 is not an isolated singularity, we can associate to the singularity a well-defined stable Hamiltonian structure on S^3, provided that f describes a Seifert fibration on S^3, L being a multi-link in this fibration. This condition is satisfied, for example, when f is complex analytic or f is given as g\\bar{h} with g and h being complex analytic. If the link is already fibered, the stable Hamiltonian structure is nothing but the contact structure mentioned above. Our construction is in fact far more general: given a Seifert multi-link (not necessarily associated to a map from R^4 to R^2) in a Seifert fibered 3-manifold, we build a well-defined stable Hamiltonian structure on the 3-manifold.

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Title: The complex of HNN-extensions associated to the free group of rank n
Speaker: Prof. Suhas Jaykumar Pandit ICTP, Trieste
Date: 17 January 2013
Time: 3.30 pm -4.30 pm
Venue: Department of Mathematics, LH-111

In this talk, we shall discuss the complex of HNN - extensions associated to the free group F_n of finite rank n. We shall sketch a proof the following result The group of simplicial automorphisms of this complex is isomorphic to the group Out(F_n) of outer automorphisms of the free group F_n of rank n.

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Title: Rigidity and Regularity of Holomorphic Mappings
Speaker: Mr. G. P. Balakumar
Date: 07 January 2013
Time: 4 - 5pm
Venue: Department of Mathematics, LH III

This talk will be on two themes that illustrate the rigidity and regularity of holomorphic mappings. The first part will deal with results concerning the smoothness of continuous CR (Cauchy – Riemann) mappings; in particular, that of Lipschitz continuous CR mappings from h-extendible/semi-regular hypersurfaces into certain Levi co-rank one hypersurfaces, in C^n. The second part will deal with the classification of Kobayashi hyperbolic, finite type rigid polynomial domains with abelian automorphism group in C^3.

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Title: Diophantine approximation, arithmetic groups, and ergodic theory
Speaker: Prof Amos Nevo Technion, Israel
Date: 02 January 2013
Time: 4:00 pm- 5:00pm
Venue: Department of Mathematics, LH-III

One of the main goals of classical metric Diophantine approximation is to quantify the denseness of the rational numbers in the real numbers, or more generally, of Q^d in R^d. An equally natural problem is to quantify the denseness of the rational points on the sphere, and more generally, rational points in other compact and non-compact algebraic sub-varieties in R^d. We will describe a solution to this problem for a large class of homogeneous varieties.

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Title: Mean ergodic theorems : from amenable to non-amenable groups
Speaker: Prof Amos Nevo Technion, Israel
Date: 31 December 2012
Time: 4:00 pm- 5:00pm
Venue: Department of Mathematics, LH-I

We will trace the evolution of the mean ergodic theorem, from its original formulation by von-Neumann to some very recent formulations valid in the context of algebraic groups and their lattice subgroups. We will then present a variety of recent applications of mean ergodic theorems, particularly to counting lattice points.

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Title: Affine Stratification Number and Moduli Space of Curves
Speaker: Dr. Chitrabhanu Chaudhuri Northwestern university
Date: 19 December 2012
Time: 4:00 pm- 5:00pm
Venue: Department of Mathematics, LH-I

The affine stratification number of a variety is a measure of how far a variety is from being affine and how close it is to being projective. I shall talk about a certain filtration on the moduli space of curves and the affine stratification number of the open sets occurring in the filtration. This will lead to some cohomology computations where we shall make use of the natural operad structure on the homology of the moduli spaces as well as the some mixed hodge theory.

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Title: Construction of Jones Polynomial for Knots (via Tangles)
Speaker: T. V. H. Prathamesh
Date: 14 December 2012
Time: 2.30 pm
Venue: LH-I, Department of Mathematics

Jones Polynomial is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynomial in the variable t^{1/2} with integer coefficients. We shall discuss the relationship between Jones Polynomial and representation of Knots through Tangles.

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Title: Construction of Jones Polynomial for Knots (via Tangles)
Speaker: T. V. H. Prathamesh
Date: 13 December 2012
Time: 2.30 pm
Venue: LH-I, Department of Mathematics

Jones Polynomial is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynomial in the variable t^{1/2} with integer coefficients. We shall discuss the relationship between Jones Polynomial and representation of Knots through Tangles.

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Title: Curvature inequalities for operators in the Cowen-Douglas class
Speaker: Mr. Dinesh Kumar Kesari
Date: 03 December 2012
Time: 11:00 a.m.
Venue: Department of Mathematics, LH-III

The curvature of a contraction T in the Cowen-Douglas class is bounded above by the curvature of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this talk we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle E corresponding to the operator T in the Cowen-Douglas class which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the Cowen-Douglas class.

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Title: Two studies of almost complex manifolds
Speaker: Dr. Herve Gaussier, Insitut Fourier, Grenoble
Date: 29 November 2012
Time: 3:30 p.m.
Venue: Department of Mathematics, LH-III

The talk will consist of two distinct parts. We will firt study the hyperbolicity of some domains in an almost complex manifold (M,J). In the second part we will study the question of the embeddability of compact almost complex manifolds in complex projective spaces.

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Title: Construction of Jones Polynomial for Knots (via Braid Groups and Hecke Algebras)
Speaker: T. V. H. Prathamesh
Date: 27 November 2012
Time: 3.30 pm
Venue: Department of Mathematics, LH-III

Jones Polynomial is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynomial in the variable t^{1/2} with integer coefficients. Though can be computed easily in terms of what are called skein relations, it originally arose from a studying a particular kind of a ‘trace’ of braid representations into an algebra derived as the quotient of a group ring of braid group. We shall discuss this construction of Jones Polynomial in the first talk. In the second part, we shall discuss the construction of Jones Polynomial from the tangle representation of Knots.

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Title: Vector bundles over hypersurfaces of projective varieties
Speaker: Mr. Amit Tripathi
Date: 26 November 2012
Time: 11:00 a.m.- 12.00 noon.
Venue: Department of Mathematics, LH-I

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Title: GROTHENDIECK INEQUALITY
Speaker: Mr. Samya Kumar Ray
Date: 21 November 2012
Time: 4:10 p.m.- 5:10 p.m.
Venue: Department of Mathematics, LH-I

Grothendieck published an extraordinary paper entitled Resume de la theorie metrique des produits tensoriels topologiques in 1953. The main result of this paper is the inequality which is commonly known as Grothendieck Inequality. Following Kirivine, in this article, we give the proof of Grothendieck Inequality. We reformulate it in different forms. We also investigate the famous Grothendieck constant KG. The Grothendieck constant was achieved by taking supremum over a special class of matrices. But our attempt will be to investigate it, considering a smaller class of matrices, namely only the positive definite matrices in this class.

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Title: Ricci flow of non-smooth spaces
Speaker: Dr. Thomas Richard IISc, Bangalore
Date: 15 November 2012
Time: 4:00 pm- 5:00 pm
Venue: Department of Mathematics, LH-III

Ricci flow is a PDE that deform the metric of a Riemannian manifold in the direction of its Ricci curvature. For compact smooth manifolds, there is a well established existence and uniqueness theory. However for some applications it can be useful to consider Ricci flows of non-smooth spaces, or metric spaces whose distance doesn’t come from a Riemannian metric. We will show that existence and uniqueness holds for the Ricci flow of compact singular surfaces whose curvature is bounded from below in the sense of Alexandrov.

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Title: The Whitney-Grauert theorem via contact geometry
Speaker: David Farris
Date: 06 November 2012
Time: 2.00 pm
Venue: Department of Mathematics, LH-III

The Whitney-Grauert theorem states that regular curves in R^2 (i.e. immersions of S^1) are classified up to regular homotopy by the winding number of the derivative. I will present Eliashberg and Geiges’s simple proof of this theorem, in which regular plane curves are realized as projections of curves in R^3 satisfying a certain geometric condition (they’ll be Legendrian curves in the standard contact structure). This is one of the simplest examples of the general pattern of lifting a purely topological problem to an equivalent but simpler problem in contact/symplectic geometry. No knowledge of contact geometry is assumed; the only prerequisite is differential forms on R^3.

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Title: On triangulating the Moduli space
Speaker: Prof Siddhartha Gadgil
Date: 30 October 2012
Time: 2.00 pm
Venue: Department of Mathematics, LH-III

I will discuss some constructions, results, questions and applications relating to the space of hyperbolic structures on a surface and its natural compactifications. I will assume that the audience understands what `hyperbolic structures on surfaces’ means.

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Title: Shift invariant spaces on the real line and on compact groups
Speaker: Prof Radha Ramakrishnan IIT, Chennai
Date: 30 October 2012
Time: 11:00 am- 12:00 noon
Venue: Department of Mathematics, Lecture Hall III

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Title: Riesz transforms associated with Heisenberg groups and Grushin operator
Speaker: Sanjay P. K. IISc, Bangalore
Date: 29 October 2012
Time: 11:30 am- 12:30 pm
Venue: Department of Mathematics, Lecture Hall I

We characterize the higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. We also prove the boundedness of the higher order Riesz transforms associated to the Hermite operator. Using transference theorems, we deduce boundedness theorems for Riesz transforms on the reduced Heisenberg group and hence also for the Riesz transforms associated to special Hermite and Laguerre expansions.

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Title: Riesz transforms associated with Heisenberg groups and Grushin operator
Speaker: Mr. Sanjay P. K. IISc, Bangalore
Date: 29 October 2012
Time: 11:30 am- 12:30 pm
Venue: Department of Mathematics, Lecture Hall I

We characterize the higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. We also prove the boundedness of the higher order Riesz transforms associated to the Hermite operator. Using transference theorems, we deduce boundedness theorems for Riesz transforms on the reduced Heisenberg group and hence also for the Riesz transforms associated to special Hermite and Laguerre expansions.

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Title: Risk-senstive control of continuous time Markov chains.
Speaker: Subhamay Saha (IISc, Mathematics)
Date: 22 October 2012
Time: 2:00pm
Venue: LH-1, Department of Mathematics, IISc

We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterise the value function via HJB equation and obtain an optimal Markov control. We do the same for infinite horizon discounted cost case. In the infinite horizon average cost case we establish the existence of an optimal stationary control under certain Lyapunov condition. We also develop a policy iteration algorithm for finding an optimal control.

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Title: Stable allocations
Speaker: Prof. Manjunath Krishnapur IISc, Bangalore
Date: 17 October 2012
Time: 4.10 pm
Venue: Department of Mathematics, LH-1

This is an informal lecture to celebrate the unprecedented event that I understand some piece of the work of some economists.

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Title: Stable allocations
Speaker: Prof. Manjunath Krishnapur IISc, Bangalore
Date: 16 October 2012
Time: 4.00 pm
Venue: Department of Mathematics, LH-1

This is an informal lecture to celebrate the unprecedented event that I understand some piece of the work of some economists.

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Title: The String topology loop product through twisting cochains
Speaker: Dr. Micah Miller IISc, Bangalore
Date: 09 October 2012
Time: 3:30 pm- 4:30 pm
Venue: Department of Mathematics, LH-III

String topology is the study of the free loop space of a manifold LM. The loop product, defined on the homology of LM, is described intuitively as a combination of the intersection product on M and loop concatenation in the based loop space of M. However, since the intersection product is well-defined only on transversally intersecting chains, this description is incomplete. Brown’s theory of twisting cochains provides a chain model of a bundle in terms of the chains on the base and chains on the fiber. We extend this theory so that it can be applied to provide a model of the free loop space. We give a precise definition of the loop product defined at the chain level.

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Title: A Google Course-builder course - Hyperbolic Spaces and Groups
Speaker: Siddhartha Gadgil
Date: 05 October 2012
Time: 3:00 p.m.
Venue: LH-III, Department of Mathematics

Google has recently released open source software called `course-builder’ (at https://code.google.com/p/course-builder/) to make interactive online courses consisting of videos interleaved with quizzes. In this brief presentation, I will show as an example a course-builder course I made and describe the process of making such courses. My goal is to convince that making online courses is both easy and worthwhile.

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Title: Dynamics of additional food provided predator-prey system with applications to biological control
Speaker: Prof B S R V Prasad VIT University, Vellore
Date: 20 September 2012
Time: 4:00 p.m.- 5:00 p.m.
Venue: Department of Mathematics, LH-III

Necessity to understand the role of additional food as a tool in biological control programs is being increasingly felt, particularly due to its Eco-friendly nature. In this present talk, we develop/analyse a variation of standard predator-prey model with Holling type II function response which presents predator-prey dynamics in presence of some additional food to predators. The aim is to study the consequences of providing additional food on the system dynamics. A thorough mathematical analysis reveals that handling times for the available foods play a vital role in determining the eventual state of the system. It is interesting to observe that by varying the quality (characterised by the handling times) and quantity of additional food we can not only control and limit the prey, but also limit and eradicate the predators. In the context of biological pest control, the results caution the manager on the choice of quality and quantity of the additional food used for this purpose. We further study the controllability aspects of the predator-prey system by considering quality of the additional food as the control variable. Control strategies are offered to steer the system from a given initial state to a required terminal state in a minimum time by formulating Mayer problem of optimal control. It is observed that an optimal strategy is a combination of bang-bang controls and could involve multiple switches. Properties of optimal paths are derived using necessary conditions for Mayer problem. In the light of the results evolved in this work it is possible to eradicate the prey from the system in the minimum time by providing the predator with high quality additional food, which is relevant in the pest management. In the perspective of biological conservation this study highlights the possibilities to drive the state to an admissible interior equilibrium (irrespective of its stability nature) of the system in a minimum time.

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Title: From Poisson kernels to stationary measures for random recursions
Speaker: Prof Ewa Damek Wroclaw University
Date: 14 September 2012
Time: 4:00 p.m.- 5:00 pm
Venue: Department of Mathematics, LH-I

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Title: Pricing Credit Derivatives in a Markov Modulated Market.
Speaker: Srikanth Iyer (IISc)
Date: 10 September 2012
Time: 2:00pm
Venue: LH-II, Department of Mathematics, IISc

Credit risk refers to the potential losses that can arise due to the changes in the credit quality of financial instruments. There are two approaches to pricing credit derivatives, namely the structural and the reduced form or intensity based models. In the structural approach explicit assumptions are made about the dynamics of a firm’s assets, its capital structure, debt and share holders. A firm defaults when its asset value reaches a certain lower threshold, defined endogenously within the model. In the intensity based approach the firm’s asset values and its capital structure are not modelled at all. Instead the dynamics of default are exogenously given through a default rate or intensity.

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Title: Asymptotic behavior of Poisson kernels on NA groups -Fifth of her lecture series
Speaker: Prof Ewa Damek University of Wroclaw, Wroclaw, Poland
Date: 06 September 2012
Time: 4:00 p.m.- 5:00 pm
Venue: Department of Mathematics, LH-I

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Title: Asymptotic behavior of Poisson kernels on NA groups - Fourth of her lecture series
Speaker: Prof Ewa Damek University of Wroclaw, Wroclaw, Poland
Date: 05 September 2012
Time: 4:00 p.m.- 5:00 pm
Venue: Department of Mathematics, LH-I

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Title: Asymptotic behavior of Poisson kernels on NA groups -Third Lecture
Speaker: Prof Ewa Damek University of Wroclaw, Wroclaw, Poland
Date: 04 September 2012
Time: 4:00 p.m.- 5:00 pm
Venue: Department of Mathematics, LH-I

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Title: Operator space projective tensor product
Speaker: Prof. Ajay Kumar, Dept. of Mathematics, University of Delhi
Date: 03 September 2012
Time: 3:00-4:00 pm
Venue: Department of Mathematics, LH-II

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Title: Asymptotic behavior of Poisson kernels on NA groups - Second lecture
Speaker: Prof Ewa Damek University of Wroclaw, Wroclaw, Poland
Date: 31 August 2012
Time: 4:00 p.m.- 5:00 pm
Venue: Department of Mathematics, LH-I

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Title: Asymptotic behavior of Poisson kernels on NA groups
Speaker: Prof Ewa Damek University of Wroclaw, Wroclaw, Poland
Date: 30 August 2012
Time: 4:00 p.m.- 5:00 pm
Venue: Department of Mathematics, LH-I

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Title: Matchings between point processes
Speaker: Mr. Indrajit Jana
Date: 24 August 2012
Time: 11:00 a.m.- 12:00 noon
Venue: Department of Mathematics, LH-III

We study several kinds of matching problems between two point processes. First we consider the set of integers $\\mathbb{Z}$. We assign a color red or blue with probability 1/2 to each integer. We match each red integer to a blue integer using some algorithm and analyze the matched edge length of the integer zero. Next we go to $\\mathbb{R}^{d}$. We consider matching between two different point processes and analyze a typical matched edge length $X$. There we see that the results vary significantly in different dimensions. In dimensions one and two (d=1,2), even $E[X^{d/2}]$ does not exist. On the other hand in dimensions more than two (d>2), $E[\\exp(cX^{d})]$ exist, where $c$ is a constant depends on $d$ only.

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Title: Rational points on Elliptic curves and congruences between modular forms
Speaker: Dr. Chandrakant Aribam Mathematics Institute, Heidelberg University
Date: 24 August 2012
Time: 4:00 pm- 5:00 pm
Venue: Department of Mathematics, Lecture Hall 1

Rational points on elliptic curves have found applications in cryptography and in the solution to some problems dating back to antiquity. However, we still do not know how to find an elliptic curve with as many points as possible. In this talk, we will see how the theory of modular forms (of Ramanujan) along with a recently developed theory enables one to understand this problem. Along the way, we will see how congruences between coefficients of modular forms shed light on this problem.

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Title: Fourier coefficients of Siegel modular forms
Speaker: Dr. Soumya Das
Date: 09 August 2012
Time: 4:00 pm- 5:00 pm
Venue: Department of Mathematics, Lecture Hall 1

We will discuss some questions concerning the existence of families of Siegel modular forms with some prescribed non-zero Fourier coefficients. If time permits, we also plan to discuss the question of characterizing cusp forms by the growth of their Fourier coefficients. Both are recent joint works with Siegfried Boecherer.

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Title: Fourier coefficients of Siegel modular forms
Speaker: Dr. Soumya Das Tata Institute of Fundamental research, Mumbai
Date: 09 August 2012
Time: 4:00 pm- 5:00 pm
Venue: Department of Mathematics, Lecture Hall 1

We will discuss some questions concerning the existence of families of Siegel modular forms with some prescribed non-zero Fourier coefficients. If time permits, we also plan to discuss the question of characterizing cusp forms by the growth of their Fourier coefficients. Both are recent joint works with Siegfried Boecherer.

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Title: Introduction to Harmonic analysis on NA groups
Speaker: Dr. Pratyoosh Kumar
Date: 08 August 2012
Time: 4:00 pm- 5:00 pm
Venue: Department of Mathematics, Lecture Hall 1

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Title: Birth of Integral Value Transformation (IVT) and some observations in Mathematics and in Genomics
Speaker: Prof. Pabitra Pal Choudhury, ISI, Kolkata
Date: 31 July 2012
Time: 4:00 pm- 5.00 pm
Venue: Department of Mathematics, Lecture Hall 1

Firstly, regarding Carry Value Transformation (CVT) some mathematical observations will be discussed. In using mathematical tools in Genomics we adopted two-way path. One is model based, another is issue based. Both these approaches will be discussed on using Human Olfactory receptors.

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Title: On the Mathematical Legacy of S. Chandrasekar
Speaker: Professor S. S. Sritharan, Director, Center for Decision, Risk, Controls and Signals Intelligence (DRCSI), Monterey, CA
Date: 30 July 2012
Time: 4:00 pm- 5.00 pm
Venue: Department of Mathematics, Lecture Hall 1

In this talk we will discuss some of the impact of Subramanian Chandrasekhar’s work on modern applied mathematics. One of the highlight of the talk will be a discussion of Chandrasekhar’s radiative transfer theory where he developed a number of breathtaking mathematical structures such as nonlinear integral equations for the Chandrasekhar H functions and X, Y functions as well as infinite dimensional Riccati (integro-partial differential differential ) equations for the scattering matrix long before the infinite dimensional systems theory.

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Title: Some Elementary Mathematics of Integral Value Transformations (IVTs) and Its Associated Dynamical Systems.
Speaker: Dr. Sarif Hassan, Institute of Mathematics and Applications, Bhubaneswar
Date: 30 July 2012
Time: 2:00 pm- 3.00 pm
Venue: Department of Mathematics, Lecture Hall 1

Some basic algebraic structures on the set of 1-dimensional IVTs are introduced. Then discrete dynamical systems are defined through IVT maps and a report on convergence of the dynamical systems has been made. Finally, some problems which are unsolved yet in the domain are discussed.

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Title: Some applications of polynomial knots.
Speaker: Prof. Rama Mishra, IISER, Pune
Date: 25 July 2012
Time: 4:00 pm- 5.00 pm
Venue: Department of Mathematics, Lecture Hall 1

Polynomial knots were introduced to represent knots in 3 space by simple polynomial equations. In this talk we will discuss how the degrees of these equations can be used in deriving information of some important knot invariants.

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Title: Analytic continuation in several complex variables
Speaker: Mr. Chandan Biswas
Date: 17 July 2012
Time: 10:00 - 11:00 a.m.
Venue: Department of Mathematics, LH-1

We wish to study those domains in $\mathbb{C}^n$, for $n\geq 2$, the so-called domains of holomorphy, which are in some sense the maximal domains of existence of the holomorphic functions defined on them. We shall demonstrate that this study is radically different from that of domains in $\mathbb{C}$ by discussing some examples of special types of domains in $\mathbb{C}^n$, $n\geq 2$, such that every function holomorphic on them extends to a strictly larger domain. This leads to Thullen’s construction of a domain (not necessarily in $\mathbb{C}^n$) spread over $\mathbb{C}^n$, the so-called envelope of holomorphy, which fulfills our criteria. With the help of this abstract approach we shall give a characterization of the domains of holomorphy in $\mathbb{C}^n$.The aforementioned characterization (holomorphic convexity) is very difficult to check. This calls for other (equivalent) criteria for a domain in $\mathbb{C}^n$, $n\geq 2$, to be a domain of holomorphy. We shall survey these criteria. We shall sketch those proofs of equivalence that rely on the first part of our survey: namely, on analytic continuation theorems. If a domain $\Omega\subset \mathbb{C}^n$, is not a domain of holomorphy, we would still like to explicitly describe a domain strictly larger than $\Omega$ to which all functions holomorphic on $\Omega$ continue analytically. One tool that is used most often in such constructions is called “Kontinuitaetssatz”. It has been invoked, without any clear statement, in many works on analytic continuation. The basic (unstated) principle that seems to be in use in these works appears to be a folk theorem. We shall provide a precise statement of this folk Kontinuitaetssatz and give a proof of it.

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Title: Homogeneous dynamics and number theory
Speaker: Dr. Anish Ghosh University of East Anglia
Date: 17 July 2012
Time: 4:00 pm- 5:00 pm
Venue: Department of Mathematics, Lecture Hall 1

I will discuss some instances of the interplay between dynamics on homogeneous spaces of algebraic groups and Diophantine approximation, with an emphasis on recent developments. The latter includes joint work with Gorodnik and Nevo, and with Einsiedler and Lytle.

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Title: Curvature inequalities for operators in the Cowen- Douglas class
Speaker: Mr. Dinesh Kumar Keshari
Date: 13 July 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall 1

The curvature of a contraction T in the Cowen-Douglas class is bounded above by the curvature of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this talk we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle E corresponding to the operator T in the Cowen-Douglas class which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the Cowen-Douglas class.

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Title: Relative Symplectic Caps, 4-Genus and Fibered Knots.
Speaker: Mr. Dheeraj Kulkarni
Date: 13 July 2012
Time: 11.00 am- 12.00 noon
Venue: Department of Mathematics, Lecture Hall 1

The $4$-genus of a knot is an important measure of complexity, related to the unknotting number. A fundamental result used to study the $4$-genus and related invariants of homology classes is the \emph{Thom Conjecture}, proved by Kronheimer-Mrowka, and its symplectic extension due to Ozsvath-Szabo, which say that \textit{closed} symplectic surfaces minimize genus.

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Title: Complex projective structures and dynamics in moduli space
Speaker: Dr. Subojoy Gupta California Institute of Technology
Date: 13 July 2012
Time: 11:00 am- 12:00 noon
Venue: Department of Mathematics, Lecture Hall 1

We shall discuss a new result that relates grafting, which are certain deformations of complex projective structures on a surface, to the Teichmuller geodesic flow in the moduli space of Riemann surfaces. A consequence is that for any fixed Fuchsian holonomy, such geometric structures are dense in moduli space.

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Title: Complex projective structures and dynamics in moduli space
Speaker: Dr. Subojoy Gupta California Institute of Technology
Date: 12 July 2012
Time: 11:00 am- 12:00 noon
Venue: Department of Mathematics, Lecture Hall 1

We shall discuss a new result that relates grafting, which are certain deformations of complex projective structures on a surface, to the Teichmuller geodesic flow in the moduli space of Riemann surfaces. A consequence is that for any fixed Fuchsian holonomy, such geometric structures are dense in moduli space.

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Title: Extension theorems for subvarieties and vector bundles.
Speaker: Prof. G.V. Ravindra University of Missouri, St. Louis
Date: 10 July 2012
Time: 2:00 - 3:00 p.m.
Venue: Department of Mathematics, Lecture Hall 3

Let Y be a complex, projective manifold and X a smooth hyperplane section in Y. Given a submanifold Z in X, under what conditions is it cut out by a submanifold Z’ in Y. An analogous quesion can be asked for vector bundles on X: namely when is a bundle on X, the restriction of a bundle on Y.

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Title: Extension theorems for vector bundles over hypersurfaces
Speaker: Mr. Amit Tripathi
Date: 10 July 2012
Time: 3:30 - 4:30 p.m.
Venue: Department of Mathematics, Lecture Hall 3

In this thesis we study some Questions on vector bundles over hypersurfaces. More precisely, for hypersurfaces of dimension $\\geq 2$, we study the extension problem of Vector bundles. We try to find some conditions under which a vector bundle over an ample divisor of non-singular projective variety, extends as a vector bundle to an open set containing that ample divisor.

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Title: KPZ equation from certain microscopic interactions
Speaker: Prof. Sunder Sethuraman University of Arizona
Date: 29 June 2012
Time: 2:00 - 3:00 p.m.
Venue: Department of Mathematics, Lecture Hall 3

We derive a form of the KPZ equation, which governs the fluctuations of a class of interface heights, in terms of a martingale problem, as the scaling limit of fluctuation fields with respect to some particle systems such as zero range processes. This is joint work in progress with P. Goncalves and M. Jara.

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Title: Properties of tempered stable distributions
Speaker: Prof. Michael Grabchak UNC Charlotte
Date: 29 June 2012
Time: 3:15 - 4:15 p.m.
Venue: Department of Mathematics, Lecture Hall 3

Tempered stable distributions were introduced in Rosinski 2007 as models that look like infinite variance stable distributions in some central region, but they have lighter (i.e. tempered) tails. We introduce a larger class of models that allow for more variety in the tails. While some cases no longer correspond to stable distributions they serve to make the class more flexible, and in certain subclasses they have been shown to provide a good fit to data. To characterize the possible tails we give detailed results about finiteness of various moments. We also give necessary and sufficient conditions for the tails to be regularly varying. This last part allows us to characterize the domain of attraction to which a particular tempered stable distribution belongs. We will also characterize the weak limits of sequences of tempered stable distributions. If time permits, we will motivate why distributions that are stable-like in some central region but with lighter tails may show up in applications.

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Title: Masas and Bimodule Decompositions of $\rm{II}_{1}$ factors
Speaker: Dr.Kunal Mukherjee IMSc, Chennai.
Date: 28 June 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

von Neumann algebras are non commutative analogue of measure spaces. The study of maximal abelian subalgebras (masas) in finite von Neumann algebras is classical to the subject from its birth and is closely tied up with Ergodic theory. Dixmier introduced two types of masas, namely, regular (Cartan) and singular. The philosophies of these two kinds of masas until recently were regarded as being different from each other. After an introduction on the subject, we justify that the existing theories can be unified. Using techniques from Free Probability and playing with suitable amenable groups we exhibit: For each subset S of $\\mathbb{N}$ (could be empty), there exist uncountably many pairwise non conjugate (by automorphism) singular masas in the free group factors for each of which $S\\cup {\\infty\\}$ arises as its Pukanzsky invariant (multiplicity function). If time permits, some other issues related to mixing, coarse bimodules, and Banach’s problem on simple Lebesgue spectrum will be addressed.

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Title: Masas and Bimodule Decompositions of $\rm{II}_{1}$ factors
Speaker: Dr. Kunal Mukherjee IMSc, Chennai.
Date: 28 June 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

von Neumann algebras are non commutative analogue of measure spaces. The study of maximal abelian subalgebras (masas) in finite von Neumann algebras is classical to the subject from its birth and is closely tied up with Ergodic theory. Dixmier introduced two types of masas, namely, regular (Cartan) and singular. The philosophies of these two kinds of masas until recently were regarded as being different from each other. After an introduction on the subject, we justify that the existing theories can be unified. Using techniques from Free Probability and playing with suitable amenable groups we exhibit: For each subset S of $\\mathbb{N}$ (could be empty), there exist uncountably many pairwise non conjugate (by automorphism) singular masas in the free group factors for each of which $S\\cup {\\infty\\}$ arises as its Pukanzsky invariant (multiplicity function). If time permits, some other issues related to mixing, coarse bimodules, and Banach’s problem on simple Lebesgue spectrum will be addressed.

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Title: Rigidity and Regularity of Holomorphic Mappings.
Speaker: Mr. G. P. Balakumar
Date: 22 June 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

This talk will be on two themes that illustrate the rigidity and regularity of holomorphic mappings. The first part will deal with results concerning the smoothness of continuous CR (Cauchy – Riemann) mappings; in particular, that of Lipschitz continuous CR mappings from h-extendible/semi-regular hypersurfaces into certain Levi co-rank one hypersurfaces, in C^n. The second part will deal with the classification of Kobayashi hyperbolic, finite type rigid polynomial domains in C^3.

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Title: Face numbers of simplicial cell manifolds
Speaker: Prof. Mikiya Masuda Osaka City University, Japan
Date: 08 June 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

A simplicial cell complex is roughly speaking a CW complex whose cells are all simplices. This notion is equivalent to that of simplicial poset in combinatorics. A simplicial complex is a simplicial cell complex, but two simplices in a simplicial cell complex may be glued together along more than one simplex on their boundaries. In this talk, I will discuss the characterization of face numbers of simplicial cell decompositions of some manifolds.

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Title: An introduction to GKM graphs
Speaker: Prof. Mikiya Masuda Osaka City University, Japan
Date: 07 June 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

The notion of a GKM graph was introduced by Guillemin-Zara [1], motivated by a result of Goresky-Kottwitz-MacPherson [2]. A GKM graph is a regular graph with directions assigned to edges satisfying certain compatibility condition. The 1-skeleton of a simple polytope provides an example of a GKM graph. One can associate a GKM graph $\\mathcal{G}_M$ to a closed manifold $M$ with an action of a compact torus satisfying certain conditions (those manifolds are often called GKM manifolds). Many important manifolds such as toric manifolds and flag manifolds are GKM manifolds. The GKM graph $\\mathcal{G}_M$ contains a lot of geometrical information on $M$, e.g. the (equivariant) cohomology of $M$ can be recovered by $\\mathcal{G}_M$. I will present an overview of some facts on GKM graphs.

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Title: Classification of the actions of the circle on 3-manifolds
Speaker: Prof. Soumen Sarkar Korea Advanced Institute of Science and Technology
Date: 06 June 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

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Title: Grushin multipliers and Toeplitz operators
Speaker: Jotsaroop Kaur
Date: 31 May 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

The Grushin operator is defined as $G:=-\Delta-|x|^2\partial_t^2$ on $\mathbb{R}^{n+1}$. We study the boundedness of the multipliers $m(G)$ of $G$ on $L^p(\mathbb{R}^{n+1})$. We prove the analogue of the Hormander-Mihlin theorem for $m(G)$. We also study the boundedness of the solution of the wave equation corresponding to $G$ on $L^p(\mathbb{R}^{n+1})$. The main tool in studying the above is the operator-valued Fourier multiplier theorem by Lutz Weis.

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Title: Matchings between point processes
Speaker: Mr. Indrajit Jana
Date: 31 May 2012
Time: 11:00 a.m. - 12:00 noon
Venue: Department of Mathematics, Lecture Hall I

We study several kinds of matching problems between two point processes. First we consider the set of integers $\\mathbb{Z}$. We assign a color red or blue with probability 1/2 to each integer. We match each red integer to a blue integer using some algorithm and analyze the matched edge length of the integer zero. Next we go to $\\mathbb{R}^{d}$. We consider matching between two different point processes and analyze a typical matched edge length $X$. There we see that the results vary significantly in different dimensions. In dimensions one and two (d=1,2), even $E[X^{d/2}]$ does not exist. On the other hand in dimensions more than two (d>2), $E[\\exp(cX^{d})]$ exist, where $c$ is a constant depends on $d$ only.

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Title: Structure of the entropy solution of a scalar conservation law with strict convex flux
Speaker: Dr. Shyam Sundar Ghoshal TIFR Centre for Applicable Mathematics, Bangalore
Date: 24 May 2012
Time: 2:30 - 3:30 p.m.
Venue: Department of Mathematics, Lecture Hall I

We prove the Structure Theorem of the entropy solution. Furthermore we obtain the shock regions each of which represents a single shock at infinity. Using the structure Theorem we construct initial data $u_0\\in C_c^\\f$ for which the solution exhibits infinitely many shocks as $t \\rightarrow \\f$. Also we have generalized the asymptotic behavior (the work of Dafermos, Liu, Kim) of the solution and obtain the rate of decay of the solution with respect to the $N$-wave.

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Title: Function Theory on non-compact Riemann surfaces
Speaker: Ms. Eliza Philip
Date: 23 May 2012
Time: 11:00 a.m. - 12:00 noon
Venue: Department of Mathematics, Lecture Hall I

Given a domain D in the complex plane and a compact subset K, Runge’s theorem provides conditions on K which guarantee that a given function that is holomorphic in some neighbourhood of K can be approximated on K by a holomorphic function on D. We look at an analogous theorem on non-compact Riemann surfaces, i.e., Runge’s approximation theorem, stated and proved by Malgrange. We revisit Malgrange’s proof of the theorem, invoking a very basic result in distribution theory: Weyl’s lemma. We look at two main applications of Runge’s theorem. Firstly, every open Riemann surface is Stein and secondly the triviality of holomorphic vector bundles on non-compact Riemann surfaces. Next, we look at the Gunning-Narasimhan theorem which states that every open (connected) Riemann surface can be immersed into $\\mathbb{C}$. We discuss the proof of this theorem as well, which depends on Runge’s theorem too. Finally we contrast the compact case to the non-compact case, by showing that every compact Riemann surface can be embedded into a large enough complex projective space.

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Title: The role of potential theory in complex dynamics
Speaker: Ms. Choiti Bandyopadhyay
Date: 23 May 2012
Time: 4:00 p.m. - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

Potential theory is the name given to the broad field of analysis encompassing such topics as harmonic and subharmonic functions, the Dirichlet problem, Green’s functions, potentials and capacity. We wish to gain a deeper understanding of complex dynamics using the tools and techniques of potential theory, and we will restrict ourselves to the iteration of holomorphic polynomials.

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Title: On the stability of certain Riemannian functionals
Speaker: Ms. Soma Maity
Date: 22 May 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

Let $M$ be a closed smooth manifold. Consider the space of Riemannian metrics $\\mathcal{M}$ on $M$. A real valued function on $\\mathcal{M}$ is called a Riemannian functional if it remains invariant under the action of the group of diffeomorphisms of $M$ on $\\mathcal{M}$. We will discuss some geometric properties of the critical points of certain natural Riemannian functionals in this lecture.

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Title: On the role of the Bargmann transform in uncertainty principles
Speaker: Rahul Garg
Date: 21 May 2012
Time: 11:00 a.m. - 12:00 noon
Venue: Department of Mathematics, Lecture Hall I

We consider functions $f$ on $\mathbb{R}^n$ for which both $f$ and their Fourier transforms $\hat{f}$ are bounded by the Gaussian $e^{-\frac{a}{2}|x|^2}$ for some $0<a<1$. Using the Bargmann transform, we show that their Fourier-Hermite coefficients have exponential decay. This is an extension of the one dimensional result of M. K. Vemuri, in which sharp estimates were proved. In higher dimensions, we obtain the analogous result for functions $f$ which are $O(n)$-finite. Here by an $O(n)$-finite function we mean a function whose restriction to the unit sphere $S^{n-1}$ has only finitely many terms in its spherical harmonic expansion. Some partial results are proved for general functions. As a corollary to these results, we obtain Hardy’s uncertainty principle. An analogous problem is studied in the case of Beurling’s uncertainty principle.

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Title: Projective modules and complete intersection--a brief survey
Speaker: Prof. N. Mohan Kumar Washington University in St. Louis, USA
Date: 18 May 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

I will discuss some of the results on projective modules and complete intersections spanning a few decades. So, necessarily, the details have to be sketchy. But, I hope to give the flavour and some of the still persistent questions in the field.

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Title: Inverse semigroups and the Cuntz-Li algebras
Speaker: Prof. S. Sundar Indian Stastical Institute, Delhi
Date: 15 May 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

Let R be an integral domain such that every non-zero quotient R/mR is finite. Consider the unitaries and isometries on \\ell^{2}(R) induced by the addition and the multiplication operation of the ring R. The C-algebra generated by these unitaries and isometries is called the ring C-algebra and was studied by Cuntz and Li.

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Title: Joint eigenfunctions on the Heisenberg group and support theorems on $\mathbb{R}^n$
Speaker: Mr. Amit Samanta
Date: 15 May 2012
Time: 11:00 a.m. - 12:00 noon
Venue: Department of Mathematics, Lecture Hall I

This work is concerned with two different problems in harmonic analysis, one on the Heisenberg group and other on $\\mathbb{R}^n$, as described in the following two paragraphs respectively.

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Title: The L-4 norm of Hecke cusp forms
Speaker: Prof. Rizwanur Khan Georg-August Universitaet Goettingen, Germany
Date: 04 May 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

This talk is on a topic in number theory, but should be accessible to a general mathematical audience.

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Title: Curvature calculations of the operators in the Cowen-Douglas class
Speaker: Mr. Prahllad Deb
Date: 30 April 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

In a foundational paper Operators Possessing an Open Set of Eigenvalues written several decades ago, Cowen and Douglas showed that an operator T on a Hilbert space H possessing an open set W (in complex plane) of eigenvalues determines a holomorphic Hermitian vector bundle ET . One of the basic theorems they prove states that the unitary equivalence class of the operator T and the equivalence class of the holomorphic Hermitian vector bundle ET are in one to one correspondence. This correspondence appears somewhat mysterious until one detects the invariants for the vector bundle ET in the operator T and vice-versa. Fortunately, this is possible in some cases. Thus they point out that if the operator T possesses the additional property that dimension of the eigenspace at each point w in W is 1, then the map f on W, sending w to ker(T-w), admits a non-zero holomorphic section, say S, and therefore defines a line bundle LT on W.It is well known that the curvature KL of a line bundle LT is a complete invariant for the line bundle LT . On the other hand, define

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Title: Analytic continuation in several complex variables
Speaker: Mr. Chandan Biswas
Date: 26 April 2012
Time: 11:00 a.m. - 12:00 noon
Venue: Department of Mathematics, Lecture Hall I

We wish to study those domains in $\\mathbb{C}^n$, for $n\\geq 2$, the so-called domains of holomorphy, which are in some sense the maximal domains of existence of the holomorphic functions defined on them. We shall demonstrate that this study is radically different from that of domains in $\\mathbb{C}$ by discussing some examples of special types of domains in $\\mathbb{C}^n$, $n\\geq 2$, such that every function holomorphic on them extends to a strictly larger domain. This leads to Thullen’s construction of a domain (not necessarily in $\\mathbb{C}^n$) spread over $\\mathbb{C}^n$, the so-called envelope of holomorphy, which fulfills our criteria. With the help of this abstract approach we shall give a characterization of the domains of holomorphy in $\\mathbb{C}^n$.

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Title: Analyzing credit risk models in a regime-switching market
Speaker: Mr. Tamal Banerjee
Date: 25 April 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

Recently, the financial world witnessed a series of major defaults by several institutions and banks. Therefore, it is not at all surprising that credit risk analysis has turned out to be one of the most important aspects of study in the finance community. As credit derivatives are long term instruments, they are affected by the changes in the market conditions. Thus, it is appropriate to take into consideration the cyclical effects of the market. This thesis addresses some of the important issues in credit risk analysis for a regime-switching market.

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Title: Discrete series representation of semisimple Lie groups
Speaker: Prof. R. Parthasarathy Bharathiar University
Date: 16 April 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

Two key steps devised by Harish Chandra for his construction of the global characters of discrete series for a non-compact real semisimple Lie group involve

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Title: Discrete series representation of semisimple Lie groups
Speaker: Prof. K. Parthasarathy Ramanujan Institute for Advanced Study, University of Madras
Date: 16 April 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

Two key steps devised by Harish Chandra for his construction of the global characters of discrete series for a non-compact real semisimple Lie group involve

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Title: Comparison results for first-order FEMs
Speaker: Dr. Mira Schedensack Humboldt University, Berlin
Date: 28 March 2012
Time: 2:30 - 3:30 p.m.
Venue: Department of Mathematics, Lecture Hall I

Please see the attachment to this e-mail.

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Title: Quasi-optimal adaptive pseudostress approximation of the Stokes equations
Speaker: Dr. Dietmar Gallistl Humboldt University, Berlin
Date: 28 March 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

Please see the attachment to this e-mail.

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Title: Topological rigidity
Speaker: Prof. Thomas Farrell SUNY at Binghamton, U.S.A.
Date: 27 March 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall III

Title: Topological Rigidity

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Title: Some representations of the discrete Heisenberg group
Speaker: Prof. Gerald B. Folland University of Washington
Date: 01 March 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

The operators $f(t) \\rightarrow f(t-a)$ and $f(t) \\rightarrow e^{2\\pi bt} f(t)$ on $L^2(\\mathbb R)$ generate unitary representations of the discrete Heisenberg group $H$ with central character $e^{2\\pi abz}$. What are the irreducible representations of $H$ with this central character, and how can one synthesize the representation just described from them ? When $ab$ is rational, the answers are quite straightforward, but when $ab$ is irrational things are much more complicated. We shall describe results in both cases.

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Title: Some representations of the discrete Heisenberg group
Speaker: Prof. Gerald B. Folland University of Washingtom
Date: 01 March 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

The operators $f(t) \\rightarrow f(t-a)$ and $f(t) \\rightarrow e^{2\\pi bt} f(t)$ on $L^2(\\mathbb R)$ generate unitary representations of the discrete Heisenberg group $H$ with central character $e^{2\\pi abz}$. What are the irreducible representations of $H$ with this central character, and how can one synthesize the representation just described from them ? When $ab$ is rational, the answers are quite straightforward, but when $ab$ is irrational things are much more complicated. We shall describe results in both cases.

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Title: Lifting of model structures to fibred categories
Speaker: Prof. Abhishek Banerjee Ohio State University, U.S.A.
Date: 27 February 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

A fibred category consists of a functor $p:\mathbf N\longrightarrow \mathbf M$ between categories $\mathbf N$ and $\mathbf M$ such that objects of $\mathbf N$ may be pulled back along any arrow of $\mathbf M$. Given a fibred category $p:\mathbf N\longrightarrow \mathbf M$ and a model structure on the base category $\mathbf M$, we show that there exists a lifting of the model structure on $\mathbf M$ to a model structure on $\mathbf N$. We will refer to such a system as a fibred model category and give several examples of such structures. We show that, under certain conditions, right homotopies of maps in the base category $\mathbf M$ may be lifted to right homotopic maps in the fibred category. Further, we show that these lifted model structures are well behaved with respect to Quillen adjunctions and Quillen equivalences. Finally, we show that if $\mathbf N$ and $\mathbf M$ carry compatible closed monoidal structures and the functor $p$ commutes with colimits, then a Quillen pair on $\mathbf M$ lifts to a Quillen pair on $\mathbf N$.

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Title: An invitation to large deviation theory
Speaker: Prof. S.S. Sritharan Center for Decision, Risk, Controls & Signals Intelligence Naval Postgraduate School Monterey, California, USA
Date: 23 February 2012
Time: 10:00 - 11:00 a.m.
Venue: Department of Mathematics, Lecture Hall I

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Title: Hurwitz equivalence: some approaches
Speaker: Prof. Siddhartha Gadgil IISc
Date: 22 February 2012
Time: 3:00 - 4:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

Hurwitz equivalence is a simple algebraic relation on the set of n-tuples in a group G. This and its generalizations are related to important problems in topology. I discuss some approaches to understanding Hurwitz equivalence.

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Title: Representations of semisimple Lie groups
Speaker: Prof. Jyoti Sengupta TIFR Mumbai
Date: 20 February 2012
Venue: Department of Mathematics, Lecture Hall I

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Title: On the lumped mass finite element method for parabolic problems
Speaker: Prof. Vidar Thomee Chalmers University of Technology Gothenburg, Sweden
Date: 08 February 2012
Time: 3:00 - 4:00 p.m.
Venue: Department of Mathematics, Lecture Hall III

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Title: Liouvillian Extensions and the Galois Theory of Linear Differential Equations
Speaker: Prof. Varadharaj Ravi Srinivasan Catholic University of America Washington, D.C.
Date: 30 January 2012
Time: 3:00 - 4:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

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Title: Commuting differential operators on Lie groups and spectral multipliers
Speaker: Prof. Alessio Martini Universitaet zu Kiel
Date: 27 January 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

Let D_1,…D_n be a system of commuting, formally self-adjoint, left invariant operators on a Lie group G. Under suitable hypotheses, we show that D_1,…D_n are essentially self-adjoint on L^2(G) and admit a joint spectral resolution, and we characterize their joint L^2 spectrum as the set of eigenvalues corresponding to a class of generalized joint eigenfunctions. Moreover, in the case G is a homogeneous group and D_1,…D_n are homogeneous, we obtain L^p-boundedness results for operators of the form m(D_1,…D_n), analogous to the Mihlin-Hormander and Marcinkiewicz multiplier theorems.

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Title: Joint spectral multipliers on nilpotent Lie groups
Speaker: Prof. Alessio Martini Universitaet zu Kiel
Date: 25 January 2012
Time: 4:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

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Title: The chiral boson and function theory on the unit disc
Speaker: Prof. T.R. Ramadas ICTP, Trieste
Date: 04 January 2012
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

Conformal field theories (CFTs) are related (in Mathematics) to algebraic geometry, infinite-dimensional Lie algebras and probability, and (in Physics) to critical phenomena and string theory. From a mathematical point of view, much of the formalisation has been from the point of view of algebra – in fact using formal power series. I will give a denition of the simplest chiral or holomorphic CFT using elementary function theory. If time permits, I will also explain operator product expansions.

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Title: The $Cos^\lambda$ transform as intertwining operator between generalized principal series representations of SL(n+1,K)
Speaker: Prof. Angela Pasquale Universite Paul Verlaine - Metz
Date: 23 December 2011
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

The $Cos^\\lambda$ transform on real Grassmann manifolds was first studied in convex geometry. The definition of this integral transform has been later extended to Grassmann manifolds over $\\mathbb K$, where $\\mathbb K$ denotes the reals, the complex numbers or the quaternions.

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Title: An overview of discontinuous Petrov-Galerkin stabilization techniques
Speaker: Prof. Jay Gopalakrishnan Portland State University
Date: 19 December 2011
Time: 4:00 - 5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

We introduce the concept of optimal test functions that guarantee stability of resulting numerical schemes. Petrov-Galerkin methods seek approximate solutions of boundary value problems in a trial space by weakly imposing all equations via a (possibly different) test space. A basic design principle is that while trial spaces must have good approximation properties, the test space must be chosen for stability. The optimal test functions are those that realize discrete stability constants equal to those in the wellposedness estimates for the undiscretized boundary value problem. When such functions are used within an ultra-weak variational formulation, we obtain Discontinuous Petrov-Galerkin (DPG) methods that exhibit remarkable stability properties. We present the first complete theory for the DPG for Laplace’s equation as well as numerical results for other more complex applications.

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Title: A nice group structure on certain orbit spaces of unimodular rows
Speaker: Prof. Anuradha Garge Centre for Excellence in Basic Sciences Mumbai
Date: 15 December 2011
Time: 11:00 a.m. - 12:00 noon
Venue: Department of Mathematics, Lecture Hall I

In this talk, we will begin with the definition of a unimodular row and its relation to Serre’s problem on projective modules. We will then see under what conditions group structures exist on orbit spaces of unimodular rows under elementary action.

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Title: Roots of Dehn twists
Speaker: Prof. Kashyap Rajeevsarathy IISER Bhopal
Date: 13 December 2011
Time: 11:00 a.m. - 12:00 noon
Venue: Department of Mathematics, Lecture Hall I

Let $F$ be a closed orientable surface of genus $g \\geq 2$ and $C$ be a simple closed curve in $F$. Let $t_C$ denote a left-handed Dehn twist about $C$. When $C$ is a nonseparating curve, D. Margalit and S. Schleimer showed the existence of such roots by finding elegant examples of roots of $t_C$ whose degree is $2g + 1$ on a surface of genus $g + 1$. This motivated an earlier collaborative work with D. McCullough in which we derived conditions for the existence of a root of degree $n$. We also showed that Margalit-Schleimer roots achieve the maximum value of $n$ among all the roots for a given genus. Suppose that $C$ is a separating curve in $F$. First, we derive algebraic conditions for the existence of roots in Mod$(F)$ of the Dehn twist $t_C$ about $C$. Finally, we show that if $n$ is the degree of a root, then $n \\leq 4g^2 + 2g$, and for $g \\geq 10$, $n \\leq \\frac{16}{5}g^2+ 12g + \\frac{45}{4}$.

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Title: Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture--Part II
Speaker: Prof. Jean-Pierre Demailly Institut Fourier, Universite de Grenoble France
Date: 24 November 2011
Time: 4:00-5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

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Title: Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture--Part I
Speaker: Prof. Jean-Pierre Demailly Institut Fourier, Universite de Grenoble France
Date: 23 November 2011
Time: 4:00-5:00 p.m.
Venue: Department of Mathematics, Lecture Hall I

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Title: Dilations, functional model and a complete unitary invariant of a $\Gamma$-contraction
Speaker: Sourav Pal Department of Mathematics, IISc
Date: 21 November 2011
Time: 3:30-4:30 p.m.
Venue: Department of Mathematics, Lecture Hall I

In this talk, we shall define $\\Gamma$-contractions, which were introduced by Jim Agler and Nicholas Young. We shall construct an explicit $\\Gamma$-isometric dilation of a $\\Gamma$-contraction and produce a genuine functional model. A crucial operator equation has to be solved for constructing such a dilation. We shall show how the existence of such a solution characterizes a $\\Gamma$-contraction. This solution, which is unique, also provides a complete unitary invariant.

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Title: Challenges in high dimensional Bayesian nonparametrics and some possible solutions
Speaker: Prof. Anjishnu Banerjee Duke University, USA
Date: 20 October 2011
Time: 11:30 a.m.-12:30 p.m.
Venue: Lecture Hall III, Department of Mathematics

Large dimensional data presents many challenges for statistical modeling via Bayesian nonparametrics, both with respect to theroetical issues and computational aspects. We discuss some models that can accomodate large dimensional data and have attractive theoretical properties, specially focussing on kernel partition processes, which are a generalization of the well known Dirichlet Processes. We discuss issues of consistency. We then move onto some typical computational problems in Bayesian nonparametrics, focussing initially on Gaussian processes (GPs). GPs are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use is the expensive computation, typically O($n^3$) in performing the necessary matrix inversions with $n$ denoting the number of data points. In large data sets, data storage and processing also lead to computational bottlenecks and numerical stability of the estimates and predicted values degrades with $n$. To address these problems, a rich variety of methods have been proposed, with recent options including predictive processes in spatial data analysis and subset of regressors in machine learning. The underlying idea in these approaches is to use a subset of the data, leading to questions of sensitivity to the subset and limitations in estimating fine scale structure in regions that are not well covered by the subset. Partially motivated by the literature on compressive sensing, we propose an alternative random projection of all the data points onto a lower-dimensional subspace, which also allows for easy parallelizability for further speeding computation. We connect this with a wide class of matrix approximation techniques. We demonstrate the superiority of this approach from a theoretical perspective and through the use of simulated and real data examples. We finally consider extensions of these approaches for dimension reduction in other non parametric models.

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Title: Sampling and meta-learning for function reconstruction -- Case study: blood glucose prediction
Speaker: Prof. Sivananthan Sampath Radon Institute for Computational and Applied Mathematics Linz, Austria
Date: 19 October 2011
Time: 4:00-5:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

In this talk, we discuss two problems: the sampling problem for a given class of functions on $\mathbb{R}$ (direct problem) and the reconstruction of a function from finite samples (inverse problem). In the sampling problem, we are given a class of functions $V\subset L^2(\mathbb{R})$ and one seeks to find sets of discrete samples such that any $f$ in $V$ can be completely recovered from its values at the sample points. Here we address the sampling problem for the class of functions $V = V(\varphi)$, the (integer) shift invariant space defined by a generator $\varphi$ with some general assumption. In the second problem, we discuss the problem of reconstruction of a real-valued function $f$ on $X\subset \mathbb{R}^d$ from the given data $\{(x_i,y_i)\}_{i=1}^n\subset X\times\mathbb{R}$, where it is assumed that $y_i=f(x_i)+\xi_i$ and $(\xi_1,…,\xi_n)$ is a noise vector. In particular, we are interested in reconstructing the function at points outside the closed convex hull of $\{x_1,…,x_n\}$, which is the so-called extrapolation problem. We consider this problem in the framework of statistical learning theory and regularization networks. In this framework, we address the major issues: how to choose an appropriate hypothesis space and regularized predictor for given data through a meta-learning approach. We employ the proposed method for blood glucose prediction in diabetes patients. Further, using real clinical data, we demonstrate that the proposed method outperforms the state-of-art (time series and neural-network-based models).

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Title: Limiting behaviour of sample autocovariance matrix
Speaker: Prof. Arup Bose ISI Kolkata
Date: 18 October 2011
Time: 11:30 a.m.-12:30 p.m.
Venue: Department of Mathematics, Lecture Hall III

The empirical spectral distribution (ESD) of the sample variance covariance matrix of i.i.d. observations under suitable moment conditions converges almost surely as the dimension tends to infinity. The limiting spectral distribution (LSD) is universal and is known in closed form with support [0,4].

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Title: Representations of Symmetric Groups via the RSK Correspondence
Speaker: Prof. Amritanshu Prasad IMSc, Chennai
Date: 23 September 2011
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

I will explain how the purely combinatorial Robinson-Schensted-Knuth correspondence can be used to give a simple proof of the classification of irreducible representations of symmetric groups in the semisimple case. It turns out that all the standard results in the representation theory of symmetric groups can be recovered using this approach.

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Title: Regularization by 1/2-Laplacian and Vanishing Viscosity Limit for HJB Equations
Speaker: Prof. Imran Biswas TIFR Centre for Applicable Mathematics
Date: 16 September 2011
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

We investigate the regularizing effect of adding small fractional Laplacian, with critical fractional exponent 1/2 , to a general first order HJB equation. Our results include some regularity estimates for the viscosity solutions of such perturbations, making the solutions classically well-defined. Most importantly, we use these regularity estimates to study the vanishing viscosity approximation to first order HJB equations by 1/2-Laplacian and derive an explicit rate of convergence for the vanishing viscosity limit.

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Title: Ergodicity of the geodesic flow of the Weil-Petersson metric
Speaker: Prof. Keith Burns Northwestern University
Date: 19 August 2011
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

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Title: The Goldman Bracket and Intersection Numbers II
Speaker: Prof. Siddhartha Gadgil IISc
Date: 17 August 2011
Time: 2:00-3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

I shall give more details of the relation of intersections to hyperbolic geometry and give a sketch of the proof of the main theorem. I shall also outline to the relation of intersection numbers to the so-called Hurwitz equivalence, and hence to smooth 4-manifolds.

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Title: The Goldman Bracket and Intersection Numbers
Speaker: Prof. Siddhartha Gadgil IISc
Date: 08 August 2011
Time: 2:00-3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

The Goldman bracket associates a Lie Algebra to closed curves on a surface. I shall describe the bracket and its basic properties. I shall also sketch some joint work with Moira Chas, where we show that the Goldman bracket together with the operation of taking powers determines geometric intersection and self-intersection numbers.

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Title: Loewner matrices
Speaker: Prof. Rajendra Bhatia ISI Delhi
Date: 05 August 2011
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Let f be a smooth function on the real line. The divided difference matrices of order n, whose, (i,j)-th entries are the divided differences of f at (\\lambda_i,\\lambda_j) – where \\lambda_1,…,\\lambda_n are prescribed real numbers – are called Loewner matrices. In a seminal paper published in 1934 Loewner used properties of these matrices to characterise operator monotone functions. In the same paper he established connections between this matrix problem, complex analytic functions, and harmonic analysis. These elegant connections sent Loewner matrices into the background. Some recent work has brought them back into focus. In particular, characterisation of operator convex functions in terms of Loewner matrices has been obtained. In this talk we describe some of this work.

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Title: Clustering, Percolation and directionally convex ordering of point processes
Speaker: Prof. D. Yogeshwaran Ecole Normale Superieure - INRIA
Date: 13 July 2011
Time: 2:30-3:30 p.m.
Venue: Department of Mathematics, Indian Institute of Science, Lecture Hall I

Heuristics indicate that point processes exhibiting clustering of points have larger critical radii for the percolation of their continuum percolation models than spatially homogeneous point processes. I will explain why the dcx ordering of point processes is suitable to compare their clustering tendencies. Hence, it is tempting to conjecture that the critical radius is increasing in dcx order. We will prove the conjecture for some non-standard critical radii; however it is false for the standard critical radii. I will discuss the implications of these results. A powerful implication is that point processes dcx-smaller than a homogeneous Poisson point process admit uniformly non-degenerate lower and upper bounds on their critical radii. In fact, all the above results hold under weaker assumptions of ordering of moment measures and void probabilities of the point processes. Examples of point processes comparable to Poisson point processes in this weaker sense include determinantal and permanental point processes with trace-class integral kernels. Perturbed lattices are the most general examples of dcx sub- and super-Poisson point processes. More generally, we show that point processes dcx-smaller than a homogeneous Poisson point process exhibit phase transitions in certain percolation models based on the level-sets of additive shot-noise fields of these point process. Examples of such models are k-percolation and SINR-percolation. This is a joint work with Bartek Blaszczyszyn.

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Title: Model Theory and a few Applications
Speaker: Prof. Koushik Pal University of California, Berkeley
Date: 22 June 2011
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Model Theory, as a subject, has grown tremendously over the last few decades. Starting out as a branch of mathematical logic, it has now wide applications in most branches of mathematics, with algebra, algebraic geometry, number theory, combinatorics and even analysis, to name a few. In this talk, I will give a brief introduction to model theory, talk about the compactness theorem (one of the main tools in model theory) and how it is used, and give one famous application of model theory to algebra, namely, the Ax-Kochen Theorem, the answer to Artin’s Conjecture. Time permitting, I will talk about a few more recent results in this direction.

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Title: Clustering, Percolation and directionally convex ordering of point processes
Speaker: Prof. D. Yogeshwaran Ecole Normale Superieure - INRIA
Date: 13 June 2011
Time: 2:30-3:30 p.m.
Venue: Department of Mathematics, Indian Institute of Science, ROOM TO BE ANNOUNCED

Heuristics indicate that point processes exhibiting clustering of points have larger critical radii for the percolation of their continuum percolation models than spatially homogeneous point processes. I will explain why the dcx ordering of point processes is suitable to compare their clustering tendencies. Hence, it is tempting to conjecture that the critical radius is increasing in dcx order. We will prove the conjecture for some non-standard critical radii; however it is false for the standard critical radii. I will discuss the implications of these results. A powerful implication is that point processes dcx-smaller than a homogeneous Poisson point process admit uniformly non-degenerate lower and upper bounds on their critical radii. In fact, all the above results hold under weaker assumptions of ordering of moment measures and void probabilities of the point processes. Examples of point processes comparable to Poisson point processes in this weaker sense include determinantal and permanental point processes with trace-class integral kernels. Perturbed lattices are the most general examples of dcx sub- and super-Poisson point processes. More generally, we show that point processes dcx-smaller than a homogeneous Poisson point process exhibit phase transitions in certain percolation models based on the level-sets of additive shot-noise fields of these point process. Examples of such models are k-percolation and SINR-percolation. This is a joint work with Bartek Blaszczyszyn.

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Title: On a small quotient of a huge absolute Galois group
Speaker: Prof. Sunil K. Chebolu Illinois State University, U.S.A.
Date: 20 May 2011
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Let G be the absolute Galois group of a field that contains a primitive p-th root of unity. This is a profinite group which is a central object of study in arithmetic algebraic geometry. In joint work with Ido Efrat and Jan Minac, we have shown that a remarkably small quotient of this big group determines the entire Galois cohomology of G. As application of this result, we give new examples of profinite groups that are not realisable as absolute Galois groups of fields. I will present an overview of this work. ALL ARE CORDIALLY INVITED

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Title: Noncommutative analogues of the Fej\'er-Riesz Theorem
Speaker: Michael Dritschel
Date: 25 April 2011
Venue: LH 1, Department of Mathematics, IISc

The classical Fej\\‘er-Riesz Theorem states that a nonnegative trigonometric polynomial can be factored as the absolute square of an analytic polynomial. Indeed, the factorization can be done with an outer polynomial. Various generalizations of this result have been considered. For example, Rosenblum showed that the result remained true for operator valued trigonometric polynomials. If one instead considers operator valued polynomials in several variables, one obtains factorization results for strictly positive polynomials, though outer factorizations become much more problematic. In another direction, Scott McCullough proved a factorization result for so-called hereditary trigonometric polynomials in freely noncommuting variables (strict positivity not needed). In this talk we consider an analogue of (hereditary) trigonometric polynomials over discrete groups, and give a result which includes a strict form of McCullough’s theorem as well as the multivariable version of Rosenblum’s theorem.

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Title: Noncommutative analogues of the Fej\'er-Riesz Theorem
Speaker: Michael Dritschel
Date: 18 April 2011
Venue: LH 1, Department of Mathematics, IISc

The classical Fej\\‘er-Riesz Theorem states that a nonnegative trigonometric polynomial can be factored as the absolute square of an analytic polynomial. Indeed, the factorization can be done with an outer polynomial. Various generalizations of this result have been considered. For example, Rosenblum showed that the result remained true for operator valued trigonometric polynomials. If one instead considers operator valued polynomials in several variables, one obtains factorization results for strictly positive polynomials, though outer factorizations become much more problematic. In another direction, Scott McCullough proved a factorization result for so-called hereditary trigonometric polynomials in freely noncommuting variables (strict positivity not needed). In this talk we consider an analogue of (hereditary) trigonometric polynomials over discrete groups, and give a result which includes a strict form of McCullough’s theorem as well as the multivariable version of Rosenblum’s theorem.

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Title: Quantum Field Theory -- the Mathematics in it
Speaker: Prof. Kalyan B. Sinha JNCASR and IISc
Date: 01 April 2011
Time: 11:00 a.m. to 12:30 p.m. (first lecture)
Venue: Lecture Hall I, Department of Mathematics

Beginning with the attempts of Heisenberg and Pauli in the 1920’s, the subject grewat an astonishing speed, culminating in the remarkable predictive successof Quantum Electrodynamics.Different attemptsto bring the subjectto a sound mathematical footing (comparable to that of Quantum Mechanics)– whetheranalytic, operator-algebraic or geometric – have tastedonly partial success. These talks will try to give a bird’s-eye view of the mathematical areas (ideas)spawned by these attempts, keeping in view the recent book of Folland on this subject.

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Title: Calculus on Fractal Curves in R^n and Physical Applications
Speaker: Dr. Seema University of Pune, Pune
Date: 10 March 2011
Time: lh-i, department of mathematics indian institute of science, bangalore
Venue: 4:00-5:00

                           ALL ARE INVITED

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Title: SRB-measure leaks
Speaker: Prof. Shrihari Sridharan Chennai Mathematical Institute
Date: 07 March 2011
Time: 4:00 p.m. - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

In this talk, we shall study about the leaking rate of the Sinai-Ruelle-Bowen (SRB) measure through holes of positive measure constructed in the Julia set of hyperbolic rational maps (open dynamics). The dependence of this rate on the size and position of the hole shall be explained. For an easier and better understanding, the simple quadratic map restricted on the unit circle will be analysed thoroughly. Time permitting, we will also compute the Hausdorff dimension of the survivor set.

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Title: On the distribution of the eigenvalues of non-selfadjoint operators
Speaker: Prof. Michael Demuth University of Clausthal Germany
Date: 01 March 2011
Time: 4:00 p.m. - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Let A be a selfadjoint operator. We are interested in the discrete spectrum of B = A+M where B is non-selfadjoint. If the resolvent difference is in the Schatten class S_p, then we have an estimate on the distribution of the eigenvalues of B. By means of this estimate we can give qualitative estimates for the number of eigenvalues of B or their moments. That can be applied to Schodinger operators with complex potentials.

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Title: Feedback controls of minimal norms
Speaker: Prof. Jean-Pierre Raymond Universite Paul Sabatier, Toulouse France
Date: 23 February 2011
Time: 4:00 p.m. - 5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

In finite-dimensional control theory, feedback control using controllability Gramian goes back to results by Kleinman and Lukes in 1968 and 1970. Some years before, R. Bass characterized controls of minimal norms also using controllability Gramians. The extension of these results to infinite-dimensional systems has a long history. Surprisingly, only reversible infinite-dimensional systems have been considered in those results. We shall present existing results in the literature and we shall characterize stabilizing controls of minimal norms for parabolic systems. This is a joint work with S. Kesavan. Application to the stabilization of the Navier-Stokes equations will be given.

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Title: Stochastic Navier-Stokes Equation with Levy noise - where Harmonic Analysis and Stochastic Analysis Meet
Speaker: Prof. S. S. Sritharan Naval Postgraduate School, Monterey, USA
Date: 11 February 2011
Time: 11:15 a.m. - 12:15 p.m.
Venue: Lecture Hall I, Department of Mathematics

Certain classes of non-local pseudo-differential operators can be associated with Markov processes and this result has an infinite dimensional counterpart too. The best known example is the Levy process with its generator an integro-differential operator. In this talk we will give an introduction to stochastic Navier-Stokes equation with jump (Levy) noise and point out opportunities for harmonic as well as stochastic analysis to gain understanding in solvability theory and applications such as control and filtering theory.

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Title: On the connections between Stochastic PDE and PDE
Speaker: Prof. B. Rajeev ISI, Bangalore Centre
Date: 28 January 2011
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Stochastic partial differential equations (SPDE) are partial differential equations (PDE) with a `noise term’. One can think of these as a semi-martingale in a function space or a space of distributions with a drift (a bounded variation process involving a second order elliptic partial differential operator ) and a noise term which is a martingale. When the martingale term is suitably structured, the solutions of these SPDE’s are closely related to certain finite dimensional diffusion processes and may be viewed as generalized solutions of the classical stochastic differential equations of Ito, Stroock-Varadhan and others. In this talk [based on Rajeev and Thangavelu (2008) and Rajeev (2010)], we describe how the expected values of the solutions give rise to solutions of PDE’s associated with the diffusion.

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Title: Pseudoholomorphic curves and applications
Speaker: Prof. Herve Gaussier Institut Fourier Grenoble, France
Date: 21 January 2011
Time: 2:00-3:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

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Title: Cofinal types of ultrafilters
Speaker: Prof. Dilip Raghavan University of Toronto
Date: 21 January 2011
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

I will describe some joint work with Todorcevic on the Tukey theory of ultrafilters on the natural numbers. The notion of Tukey equivalence tries to capture the idea that two directed posets look cofinally the same, or have the same cofinal type. As such, it provides a device for a rough classification of directed sets based upon their cofinal type, as opposed to an exact classification based on their isomorphism type. This notion has recently received a lot of attention in various contexts in set theory. As background, I will illustrate the idea of rough classification with several examples, and explain how rough classification based on Tukey equivalence fits in with other work in set theory. The talk will be based on the paper Cofinal types of ultrafilters. A preprint of the paper is available on my website: http://www.math.toronto.edu/raghavan .

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Title: Extremal discs in almost complex manifolds
Speaker: Prof. Herve Gaussier Institut Fourier Grenoble, France
Date: 20 January 2011
Time: 2:30-3:30 p.m.
Venue: Lecture Hall III, Department of Mathematics

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Title: Serre's mass formula in prime degree
Speaker: Prof. Chandan Singh Dalawat HRI, Allahabad
Date: 19 January 2011
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Serre’s mass formula counts the number of totally ramified degree-$n$ extensions $E$ of a local field $F$, each extension being assigned some weight depending upon how ramified it is. We will present an elementary proof of this formula when the degree $n$ is prime.The background material will be covered, so that the talk should be accessible to a broad mathematical audience.

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Title: Serre's mass formula in prime degree
Speaker: Prof. Chandan Singh Dalawat HRI, Allahabad
Date: 18 January 2011
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

Serre’s mass formula counts the number of totally ramified degree-$n$ extensions $E$ of a local field $F$, each extension being assigned some weight depending upon how ramified it is. We will present an elementary proof of this formula when the degree $n$ is prime.The background material will be covered, so that the talk should be accessible to a broad mathematical audience.

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Title: The Brylinski Beta function
Speaker: Prof. Murali Vemuri Chennai Mathematical Institute
Date: 10 January 2011
Time: 4:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

An analogue of Brylinski’s knot beta function is defined for a submanifold of d-dimensional Euclidean space. This is a meromorphic function on the complex plane. The first few residues are computed for a surface in three dimensional space.

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Title: The Brylinski Beta function
Speaker: Prof. Murali Vemuri
Date: 10 January 2011
Time: lh 3, department of mathematics indian institute of science, bangalore
Venue: 4:00

An analogue of Brylinski’s knot beta function is defined for a submanifold of d-dimensional Euclidean space. This is a meromorphic function on the complex plane. The first few residues are computed for a surface in three dimensional space.

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Title: The tyger phenomenon for the Galerkin-truncated Burgers and Euler equations
Speaker: Prof. Uriel Frisch Observatoire de la Cote d'Azur Nice, France
Date: 24 December 2010
Time: lh 1, department of mathematics indian institute of science, bangalore
Venue: 4:00

It is shown that the solutions of inviscid hydrodynamical equations with suppression of all spatial Fourier modes having wavenumbers in excess of a threshold $\kg$ exhibit unexpected features. The study is carried out for both the one-dimensional Burgers equation and the two-dimensional incompressible Euler equation. At large $\kg$, for smooth initial conditions, the first symptom of truncation, a localized short-wavelength oscillation which we call a “tyger”, is caused by a resonant interaction between fluid particle motion and truncation waves generated by small-scale features (shocks, layers with strong vorticity gradients, etc). These tygers appear when complex-space singularities come within one Galerkin wavelength $\lambdag = 2\pi/\kg$ from the real domain and typically arise far away from preexisting small-scale structures at locations whose velocities match that of such structures. Tygers are weak and strongly localized at first - in the Burgers case at the time of appearance of the first shock their amplitudes and widths are proportional to $\kg ^{-2/3}$ and $\kg ^{-1/3}$ respectively - but grow and eventually invade the whole flow. They are thus the first manifestations of the thermalization predicted by T.D. Lee in 1952. The sudden dissipative anomaly-the presence of a finite dissipation in the limit of vanishing viscosity after a finite time $\ts$-, which is well known for the Burgers equation and sometimes conjectured for the 3D Euler equation, has as counterpart in the truncated case the ability of tygers to store a finite amount of energy in the limit $\kg\to\infty$. This leads to Reynolds stresses acting on scales larger than the Galerkin wavelength and thus prevents the flow from converging to the inviscid-limit solution. There are indications that it may be possible to purge the tygers and thereby to recover the correct inviscid-limit behaviour.

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Title: Forbidden configurations, extremal set systems, and Steiner designs
Speaker: Prof. Niranjan Balachandran Caltech U.S.A.
Date: 14 December 2010
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

One of the fundamental problems in Extremal Combinatorics concerns maximal set systems with forbidden subconfigurations. One such open problem concerns the conjecture due to Anstee and Sali on the order of maximal configurations with certain forbidden subconfigurations. I shall talk about some well known results, talk about the Anstee-Sali conjecture, and finally talk about some of my recent work concerning Steiner designs occuring as maximal forbidden configurations for certain natural choices of subconfigrations. This generalizes a result of Anstee and Barekat.

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Title: Hilbert spaces based on complex Hermite polynomials, and related quantizations
Speaker: Prof. Jean-Pierre Gazeau Universit Paris-7 Denis Diderot France
Date: 13 December 2010
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

I will report on the existence and properties of Hilbert spaces based on different families of complex, holomorphic or not, functions, like Hermite polynomials. The resulting coherent state quantizations of the complex plane will be presented. Some interesting issues will be examined, like the existence of the usual harmonic oscillator spectrum despite the absence of canonical commutation rules.

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Title: An iterated observer method for recovering the initial state for a class of PDE's
Speaker: Prof. Marius Tucsnak Institut Elie Cartan Universite Nancy-1 France
Date: 24 November 2010
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

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Title: Distributed Processing and Temporal Codes in Neuronal Networks
Speaker: Prof. Wolf Singer Director, Max Planck Institute for Brain Research Frankfurt/Main Frankfurt Institute for Advanced Studies (FIAS)
Date: 18 November 2010
Time: lh 1, department of mathematics indian institute of science, bangalore
Venue: 11:00

Higher cognitive functions require the coordination of large assemblies of

spatially distributed neurons in ever changing constellations. It is

proposed that this coordination is achieved through temporal coordination

of oscillatory activity in specific frequency bands. Since there is no

supra-ordinate command centre in the brain, the respective patterns of

synchronous activity self-organize, which has important implications on

concepts of intentionality and top down causation. Evidence will be

provided that synchronisation supports response selection by attention,

feature binding, subsystem integration, short-term memory, flexible

routing of signals across cortical networks and access to the work-space

of consciousness. The precision of synchronisation is in the millisecond

range, suggesting the possibility that information is encoded not only in

the co-variation of discharge rates but also in the precise timing of

individual action potentials. This could account for the high speed with

which cortical circuits can encode and process information. Recent studies

in schizophrenic patients indicate that this disorder is associated with

abnormal synchronisation of oscillatory activity in the high frequency

range (beta and gamma). This suggests that some of the cognitive deficits

characteristic for this disease result from deficient binding and

subsystem integration.

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Title: The Cauchy-Riemann equations in a product domain
Speaker: Prof. Debraj Chakrabarti Department of Mathermatics IIT Bombay
Date: 16 November 2010
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

An important question in complex analysis is to solve the inhomogenous Cauchy-Riemann equations (also called the d-bar equation) in a domain in C^n. The question of boundary smoothness in the d-bar problem is classically dealt with by solving the associated d-bar Neumann problem and showing that the solution operator, the $\\overline{\\partial}$-Neumann operator is compact. For many domains of interest, in particular the product domains, this approach fails. We discuss in this talk some new results on the regularity of the d-bar problem in product domains. This work is joint with Mei-Chi Shaw.

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Title: Projective Geometry and Holomorphic curves
Speaker: Prof. Siddhartha Gadgil Indian Institute of Science
Date: 22 September 2010
Time: 4:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

A geometry is a collection of lines and points satisfying the usual incidence axioms. By a theorem of Gromov, given an almost complex structure (which is `tame’) on the complex projective plane CP^2, we obtain a geometry by declaring appropriate holomorphic curves to be the lines. Ghys asked whether Desargues’s theorem (a Euclidean geometry result related to symmetry) characterises the standard complex structure. We show that this is indeed the case.

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Title: Distinguishing knots
Speaker: Prof. Siddhartha Gadgil Indian Institute of Science
Date: 17 September 2010
Time: 2:00 p.m.
Venue: Lecture Hall III, Department of Mathematics

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Title: Analytic continuation of the resolvent, resonances, and Huygens' principle for Riemannian symmetric spaces of noncompact type
Speaker: Prof. Angela Pasquale Universite Paul Verlaine--Metz France
Date: 13 September 2010
Time: 4:00-5:00 p.m.
Venue: Lecture Hall I, Department of Mathematics

The abstract of this talk has been posted at:

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Title: Triangulating the Deligne-Mumford Compactification of Riemann Surfaces
Speaker: Dr. Siddhartha Gadgil, IISc.
Date: 17 August 2010
Time: 2:00 p.m.
Venue: LH-1, Department of Mathematics

The space of all complex structures on a surface, and the Deligne-Mumford compactification of this space, play an important role in many areas of mathematics. We give a combinatorial description of a space that is homotopy equivalent to the Deligne-Mumford compactification, in the case of surfaces with at least one puncture.

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Title: The mysterious geometry of soap bubbles
Speaker: Prof. Michael Hutchings, U.C.Berkeley.
Date: 13 August 2010
Time: 4:00 p.m.
Venue: Faculty Hall, IISc.

Why are soap bubbles spherical? Why do double soap bubbles have the shape that they do (three spherical caps meeting along a circle at 120 degree angles)? The single bubble problem was solved in the 19th century, and the double bubble problem was solved a few years ago. The analogous problem for triple soap bubbles remains a mystery. We will give an introduction to these problems and their solutions (when known).

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Title: Exploring polynomial convexity of certain classes of sets
Speaker: Mr. Sushil Gorai, IISc.
Date: 14 July 2010
Time: 4:00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

It is very difficult in general to determine when a given compact in C^n, n>1, is polynomially convex. In this talk, we shall discuss polynomial convexity of some classes of sets. First, we shall consider two totally-real surfaces in C^2 that contain the origin and have distinct tangent planes there. We shall discuss how the local polynomial convexity of the union of the tangent planes at (0,0) influences local polynomial convexity of the union of the surfaces at (0,0). Secondly, we will present a condition for local polynomial convexity of unions of more than two totally-real planes in C^2 containing the origin. Next, we shall talk about pluri- subharmonicity. Using this notion we shall give a new proof of an approximation theorem of Axler and Shields and also generalize it. Polynomial convexity plays a very central role in our proof. Finally we shall discuss a characterization for (large) compact patches of smooth totally-real graphs in C^{2n} to be polynomially convex.

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Title: A study of the metric induced by the Robin function
Speaker: Mr. Diganta Borah, IISc.
Date: 09 July 2010
Time: 4:00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

Let D be a smoothly bounded pseudoconvex domain in C^n, n > 1. Using G(z, p), the Green function for D with pole at p in D, associated with the standard sum-of-squares Laplacian, N. Levenberg and H. Yamaguchi had constructed a Kahler metric (the so-called Lambda–metric) using the Robin function arising from G(z, p). The purpose of this thesis is to study this metric by deriving its boundary asymptotics and using them to calculate the holomorphic sectional curvature along normal directions. It is also shown that the Lambda–metric is comparable to the Kobayashi (and hence to the Bergman and Caratheodory metrics) when D is strongly pseudoconvex. The unit ball in C^n is also characterized among all smoothly bounded strongly convex domains on which the Lambda–metric has constant negative holomorphic sectional curvature. This may be regarded as a version of Lu-Qi Keng’s theorem for the Bergman metric.

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Title: Topological T - Duality
Speaker: Dr. Ashwin Pande Australian National University Australia.
Date: 07 July 2010
Time: 4.00 p.m.
Venue: Department of Mathematics, LH - III

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Title: Certain convolution inequalities on rank one symmetric spaces of noncompact type
Speaker: Prof Swagato Ray IIT, Kanpur
Date: 14 June 2010
Time: 4:00 pm
Venue: LH-I, Department of Mathematics

Kunze Stein inequality can be thought of as a semisimple version of Young’s inequality. A remarkable observation of M.G.Cowling and S.Meda shows that these inequalities can be naturally extended to Lorentz spaces. The final result in this direction was proved by A. Ionescu. In this talk we will try to explain the central ideas behind Kunze Stein type convolution inequalities for Lorentz spaces.

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Title: Some generalizations of Hartogs' lemma on analytic continuation
Speaker: Ms. Purvi Gupta
Date: 04 June 2010
Time: 3:30 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

It is well known that there exist domains in C^n, n > 1, such that all functions holomorphic therein extend holomorphically past the boundary. In this talk, we shall examine this surprising phenomenon by discussing refinements of the fundamental example of Hartogs. We shall look at a generalization of Hartogs’ construction discovered by Chirka. Finally, we shall provide a partial answer to a related question raised by Chirka.

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Title: Arithmeticity of complex hyperbolic lattices.
Speaker: Martin Deraux Fourier Institute, Grenoble
Date: 24 May 2010
Time: monday at 2:00 p.m. wednesday at 4:00 p.m.
Venue: LH-1 IISc Mathematics Department

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Title: Kinematical conservation laws and propagation of nonlinear waves in three dimensions
Speaker: K. R. Arun, Research student, Department of Mathematics, IISc
Date: 11 May 2010

We derive the conservation form of equations of evolution of a front propagating in three dimensions. We obtain a system of six conservation laws, known as 3-D kinematical conservation laws (KCL) in a ray coordinate system. The conservative variables of 3-D KCL are also constrained by a stationary vector constraint, known as geometric solenoidal constraint, which consists of three divergence-free type conditions. The 3-D KCL is an under-determined system, and therefore, additional closure relations are required to get a complete set of equations. We consider two closure relations for 3-D KCL: (1) energy transport equation of a weakly nonlinear ray theory (WNLRT) to study the propagation of a nonlinear wavefront, (2) transport equations of a shock ray theory (SRT) to study the propagation of a curved weak shock front. In both the cases we obtain a weakly hyperbolic system of balance laws. For the numerical simulation we use a high-resolution semi-discrete central scheme. The second order accuracy of the scheme is based on MUSCL type reconstructions and TVD Runge-Kutta time stepping procedures. A constrained transport technique is used to enforce the geometric solenoidal constraint and in all the test problems considered, the constraint is satisfied up to very high accuracy. We present the results of extensive numerical experiments, which confirm the efficiency and robustness of the method and also its ability to capture many physically realistic features of the fronts.

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Title: Some aspects of the Kobayashi and Caratheodary metrics on pseudoconvex domains.
Speaker: Ms. Prachi, IISc.
Date: 21 April 2010
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

This thesis considers two themes, both of which emanate from and involve the Kobayashi and the Carath\\‘{e}odory metric. First we study the biholomorphic invariant introduced by B. Fridman on strongly pseudoconvex domains, on weakly pseudoconvex domains of finite type in $\\mathbf C^2$ and on convex finite type domains in $\\mathbf C^n$ using the scaling method. Applications include an alternate proof of the Wong-Rosay theorem, a characterization of analytic polyhedra with noncompact automorphism group when the orbit accumulates at a singular boundary point and a description of the Kobayashi balls on weakly pseudoconvex domains of finite type in $ \\mathbf C^2$ and convex finite type domains in $ \\mathbf C^n$ in terms of Euclidean parameters. Second a version of Vitushkin’s theorem about the uniform extendability of a compact subgroup of automorphisms of a real analytic strongly pseudoconvex domain is proved for $C^1$-isometries of the Kobayashi and Carath\\‘{e}odory metrics on a smoothly bounded strongly pseudoconvex domain.

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Title: Test function realizations and Agler-Herglotz representations
Speaker: Prof. James Pickering, Newcastle University, UK
Date: 19 April 2010
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Brody hyperbolicity and homotopy theory
Speaker: Dr. Simone Borghesi
Date: 16 April 2010
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

The most immediate way to use classical homotopy theory to study topological spaces endowed with extra structures, such as complex spaces, is to forget these structures and study the underlying topological space. Usually this procedure is inadequate since what we are forgetting is not homotopy invariant nor topological invariant. There are more sophisticated approaches to use homotopy theory to try to detect different complex structures on the same topological space which prove to be effective, for instance if the topological space is a complex variety and the complex structures endow the tangent bundle of different Chern classes/numbers. A much more thorough approach can be achieved by using model category theory to provide the category of complex spaces with holomorphic maps of an homotopy theory which realizes to the ordinary topological one, it is biholomorphic but not topological invariant. These techniques have been previously implemented by Morel and Voevodsky to create the so called A^1 homotopy theory of algebraic varieties few years ago.

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Title: Generalized Calabi-Eckmann manifolds
Speaker: Prof. Parameswaran Sankaran, IMSc, Chennai.
Date: 13 April 2010
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Intersection numbers, embedded spheres and Geosphere laminations for free groups
Speaker: Dr. Suhas Pandit, IISER, Pune
Date: 13 April 2010
Time: 2:00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

Free groups and the group of their outer automorphisms have been extensively studied in analogy with (fundamental groups of) surfaces and the mapping class groups of surfaces. We study the analogue of intersection numbers of simple curves, namely the Scott-Swarup algebraic intersection number of splittings of a free group and we also study embedded spheres in $3$- manifold of the form $ M =\\sharp_n S^2 \\times S^1 $. The fundamental group of $M$ is a free group of rank $n$. This $3$-manifold will be our model for free groups. We construct geosphere laminations in free group which are analogues of geodesic laminations on a surface.

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Title: Fuglede's conjecture, Tilings and Spectra
Speaker: Prof. Shobha Madan, IIT Kanpur.
Date: 15 March 2010
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: On concave univalent functions
Speaker: Dr. Bappaditya Bhowmik
Date: 25 February 2010
Time: 11:00 a.m.
Venue: Lecture Hall - I, Dept. of Mathematics

One of the most important subclasses of the class of normalized analytic univalent functions on the open unit disc D is the class of convex functions. In this talk we will focus on meromorphic analogues of the results known for this class. I.e. we consider functions that map D conformally onto a set whose complement is a bounded convex set. We shall begin with a brief history of Livingston’s conjecture which concerns the exact set of variability of the Taylor coefficients for concave functions. Thereafter, we shall discuss some new results concerning the closed convex hull of concave functions and extreme points of it.

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Title: Can Computers do Mathematics? Ventures in Topology/Geometry
Speaker: Dr. Siddhartha Gadgil, IISc.
Date: 11 January 2010
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We discuss applications of computers to prove mathematical theorems. In particular we discuss possible future applications in Topology/Geometry. This will also be the introductory lecture to the new course `Computer Assisted Topology/Geometry’

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Title: Effective Models and Algebraic Topology II.
Speaker: Prof. Dennis Sullivan, Stony Brook.
Date: 29 December 2009
Time: 2:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Minimal intersections of curves on surfaces.
Speaker: Dr. Moria Chas, Stony Brook.
Date: 29 December 2009
Time: 11:00 a.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Negative sectional curvature and product complex structures.
Speaker: Dr. Harish Seshadri, IISc.
Date: 29 December 2009
Time: 10:00 a.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: String Topology
Speaker: Prof. Dennis Sullivan, Stony Brook.
Date: 21 December 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Can Computers do Mathematics? Ventures in Topology/Geometry
Speaker: Dr. Siddhartha Gadgil, IISc.
Date: 21 December 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We discuss applications of computers to prove mathematical theorems. In particular we discuss possible future applications in Topology/Geometry. This will also be the introductory lecture to the new course `Computer Assisted Topology/Geometry’

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Title: Algebraic structures related to the intersection of curves on surfaces
Speaker: Dr. Moria Chas, Stony Brook.
Date: 21 December 2009
Time: 2:30 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Given a surface, one can consider the set of free homotopy classes of oriented closed curves (this is the set of equivalence classes of maps from the circle into the surface, where two such maps are equivalent if the corresponding curves can be deformed one into the other.) Given a free homotopy class one can ask what is the minimum number of times (counted with multiplicity) in which a curve in that class intersects itself. This is the minimal self-intersection number of the free homotopy class. Analogously, given two classes, one can ask what is the minimum number of times representatives of these classes intersect. This is the minimal intersection number of these two classes.

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Title: Hyperbolicity of cycle spaces and Automorphism groups of flag domains
Speaker: Prof. Alan Huckleberry, Ruhr University, Bochum, Germany
Date: 11 December 2009
Time: 2:30 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

The appropriate context for algebraic-geometric realizations of holomorphic representations of a complex semisimple group is that of a compact homogeneous projective flag manifold Z = G/Q. One topic of more current interest is the study of the possibility of realizing (infinite-dimensional) unitary representations of a real form G0 of G on function- and/or cohomology-spaces of open G_0-orbits D in Z (flag domains) and their cycle spaces. After an introduction for nonspecialists, we will indicate a proof by Schubert incidence geometry of the Kobayashi hyperbolicity of the relevant cycle spaces. This will then be applied to give an exact description of the group Aut_O(D) of holomorphic automorphisms.

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Title: Realization and interpolation in the Schur class of the polydisk
Speaker: Prof. Michael Dritschel, Newcastle University, UK.
Date: 01 December 2009
Time: 4:00 p.m.
Venue: CHEP Lecture Hall

The classical realization theorem gives various characterizations of functions in the unit ball of $H^\\infty(\\mathbb D)$, the bounded analytic functions on the unit disk $\\mathbb D$, which happens to also correspond to the multipliers of Hardy space $H^2(\\mathbb D)$. This realization theorem yields an elegant way of solving the Nevanlinna-Pick interpolation problem. In the mid 80s, Jim Agler discovered an analogue of the realization theorem over the polydisk. While for $d=2$, it once again gives a characterization of the elements of the unit ball of $H^\\infty(\\mathbb D^d)$ (and so allows one to solve interpolation problems in $H^\\infty(\\mathbb D^2)$), for $d>2$, the class of functions which are realized is a proper subset of the unit ball of $H^\\infty(\\mathbb D^d)$ — the so-called Schur-Agler class.

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Title: The connection between Clifford analysis and operator theory
Speaker: Prof. Brian Jefferies, University of New South Wales, Sydney
Date: 30 November 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Clifford analysis is a higher dimensional analogue of single variable complex analysis. Although functions take values in a finite dimensional Clifford algebra, the representation formula for Clifford regular functions is simpler and more powerful than for holomorphic functions of several complex variables. The talk shows how Clifford analysis techniques can be employed in operator theory for a functional calculus of $n$-tuples of operators.

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Title: Limiting Spectral Distribution of Large Dimensional Random Matrices: Another Look at the Moment Method
Speaker: Prof. Arup Bose, ISI, Kolkata
Date: 21 October 2009
Time: 2:00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

Methods to establish the limiting spectral distribution (LSD) of large dimensional random matrices include the moment method which invokes the trace formula. Its success has been demonstrated in several types of matrices such as the Wigner matrix and the sample variance covariance matrix. In a recent article Bryc, Dembo and Jiang (2006) establish the LSD for random Toeplitz and Hankel matrices using the moment method. They perform the necessary counting of terms in the trace by splitting the relevant sets into equivalence classes and relating the limits of the counts to certain volume calculations. We develop this method further and provide a general framework to deal with symmetric patterned matrices with entries coming from an independent sequence. This approach can be extended to cover matrices of the form Ap =XX’/n where X is a pxn matrix with p going infinity and n = n(p) going to infinity and p/n going to y between 0 and infinity. The method can also be used to cover some situations where the input sequence is a suitable linear process. Several new classes of limit distributions arise and many interesting questions remain to be answered.

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Title: Buseman functions in a harmonic manifold
Speaker: Dr. Hemangi Shah, IISc.
Date: 19 October 2009
Time: 4:00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

For a noncompact complete and simply connected harmonic manifold M, we prove the analyticity of Busemann functions on M. This is the main result of this paper. An application of it shows that the harmonic spaces having minimal horospheres have the bi-asymptotic property. Finally we prove that the total Busemann function is continuous in C^\\infty topology. As a consequence of it we show that the uniform divergence of geodesics holds in these spaces.

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Title: Mean-field Limits of Interacting Particle Systems
Speaker: Dr. D. Yogeshwaran, Ecole Normale Superieure / INRIA, Paris.
Date: 02 September 2009
Time: 11.30 - 12.45
Venue: ECE 1.07

Consider a system of N interacting particles evolving over time with Markovian dynamics. The interaction occurs only due to a shared resource. I shall briefly sketch the classical tightness-existence-uniqueness approach used to prove weak convergence of the system to a limiting system as N tends to infinity. I shall illustrate another approach in more detail with the example of a nonlinear Markov chain. In the case of exchangeable particles, weak convergence of the system implies propogation of chaos i.e, in the limiting system particles evolve independently due to a deterministically shared resource.

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Title: Weighted zero-sum problems: recent progress
Speaker: Prof. S. D. Adhikari, HRI, Allahabad.
Date: 01 September 2009
Time: 4:00 p.m.
Venue: Lecture Hall - II, Dept. of Mathematics

After a brief introduction to some classical group invariants, we proceed to consider their generalizations with weights. We discuss some recent results on these weighted generalizations.

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Title: Comparison of critical percolation radii of directionally convex orderered point processes.
Speaker: Dr. D. Yogeshwaran, Ecole Normale Superieure / INRIA, Paris.
Date: 01 September 2009
Time: 4:00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

Heuristics indicate that more the clustering in a point process, worse the percolation will be. We shall in this talk see a first step towards a formal proof of this heuristic. Here is a more precise abstract of the results we shall see in the talk.

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Title: The d-th polarization constant of Rd
Speaker: Prof. Rakesh, University of Delaware
Date: 28 August 2009
Time: 4:00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

The polarization conjecture for R^d is that

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Title: A complex hyperbolic reflection group and the bimonster
Speaker: Dr. Tathagatha Basak, IPMU, Japan
Date: 21 August 2009
Time: 11:00 a.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Let R be the reflection group of the complex leech lattice plus a hyperbolic cell. Let D be the incidence graph of the projective plane over the finite field with 3 elements. Let A(D) be the Artin group of D: generators of A(D) correspond to vertices of D. Two generators braid if there is an edge between them, otherwise they commute.

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Title: Gibbs measure asymptotics
Speaker: Prof. K. B. Athreya
Date: 14 August 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Let H :R –> R. with multiple minima on R.For T> 0 consider the probability measure on R with pdf proportional to exp(–H/T). In this talk we discuss the problem of weak limits of this measure as T goes to infinity. It depends on the behaviour of H near its minima locations. Both Gaussian and stable limit laws arise as weak limits.

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Title: Interacting diffusion models and the effect of size
Speaker: Dr.Soumik Pal, University of Washington, Seattle
Date: 04 August 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Consider a multidimensional diffusion model where the drift and the diffusion coefficients for individual coordinates are functions of the relative sizes of their current value compared to the others. Two such models were introduced by Fernholz and Karatzas as models for equity markets to reflect some well-known empirically observed facts. In the first model, called ‘Rank-based’, the time-dynamics is determined by the ordering in which the coordinate values can be arranged at any point of time. In the other, named the ‘Volatility-stabilized’, the parameters are functions of the ratio of the current value to the total sum over all coordinates. We show some remarkable properties of these models, in particular, phase transitions and infinite divisibility. Relationships with existing models of queueing, dynamic spin glasses, and statistical genetics will be discussed. Part of the material is based on separate joint work with Sourav Chatterjee and Jim Pitman.

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Title: Gaussian Minkowski functionals: an overview of infinite dimensional geometry in Wiener space
Speaker: Dr. V. Sreekar
Date: 24 July 2009
Time: 4 - 5 pm.
Venue: LH-III, Department of Mathematics

Gaussian Minkowski functionals (GMFs) for reasonably smooth subsets of Euclidean spaces, are defined as coefficients appearing in the the Gaussian-tube-formula in finite dimensional Euclidean spaces. The fact that the measure in consideration here is Gaussian, itself makes the whole analysis an infinite dimensional one. Therefore, one might want to generalize the definition of Gaussian Minkowski functionals to the subsets of Wiener space which arise from reasonably smooth (in Malliavin sense) Wiener functionals. As in the finite dimensional case, we shall identify the GMFs in the infinite dimensional case, as the coefficients appearing in the tube formula in Wiener space. Finally, we shall try to apply this infinite dimensional generalization to get results about the geometry of excursion sets of a reasonably large class of random fields defined on a “smooth” manifold.

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Title: Wave Propagation on Networks
Speaker: Prof. E. Zuazua Scientific Director BCAM - Basque Center for Applied Mathematics, Spain
Date: 24 July 2009
Time: lh 1, department of mathematics indian institute of science, bangalore
Venue: 4:00

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Title: The ubiquity of the symplectic Hamiltonian equations in mechanics
Speaker: Prof. Manuel de Len Instituto de Ciencias Matemticas Consejo Superior de Investigaciones Cientificas
Date: 21 July 2009
Time: lh 1, department of mathematics indian institute of science, bangalore
Venue: 4:00

                           ALL ARE INVITED

                         Coffee/Tea: 3:45 pm

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Title: Horocycles on the modular surface and diophantine approximation
Speaker: Dr. Jayadev Athreya, Yale University
Date: 20 July 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We describe a relationship between cusp excursions of horocycles on the modular surfaces SL(2, R)/SL(2, Z) and diophantine approximation. Some of the work we discuss will be joint with G. Margulis, and some joint with Y. Cheung

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Title: Large deviations for a tagged particle in one dimensional simple exclusion.
Speaker: Prof. Sunder Sethuraman, Iowa State Univ.
Date: 07 July 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Quotient Varieties modulo Finite Groups
Speaker: Prof. S. S. Kannan, CMI
Date: 01 July 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Let $V$ be finite dimensional vector space over the field of complex numbers. Let $G$ be a finite subgroup of $GL(V)$, group of all $\mathbb{C}$- linear automorphisms of $V$. Then, the apmple generator of the Picard group of the projective space $\mathbb P(V)$ descends to the quotient variety $\mathbb{P}(V)/G$. Let $L$ denote the descent. We prove that the polarised variety $\mathbb P(V)/G, L$ is projectively normal when $G$ is solvable or $G$ is generated by pseudo reflections.

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Title: Operator Theory and Algebraic Topology
Speaker: R. G. Douglas Texas A&M University
Date: 05 June 2009
Time: l h 1, department of mathematics indian institute of science, bangalore
Venue: 4.00

About thirty-five years ago, several problems in operator theory concerning almost normal operators led L. G. Brown, P. A. fillmore and me to introduce methods and point of view from algebraic topology to solve them. By the time we were done concrete realization of K-homology was introduced as well as new insight obtained for the index theorem of Atiyah-Singer.

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Title: Systems Biology Approaches for the Environmental Biotechnology Applications
Speaker: Prof. Radhakrishnan Mahadevan Department of Chemical Engineering and Applied Chemistry University of Toronto
Date: 06 May 2009
Time: 2:00 pm
Venue: Lecture Hall I, Department of Mathematics

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Title: On spectrum and arithmetic
Speaker: Prof. C. S. Rajan, TIFR, Mumbai
Date: 20 April 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We will discuss the notion of spectrum and arithmetic of spaces, and expound on the expectation that they should mutually determine each other for the class of locally symmetric spaces associated to congruent arithmetic lattices.

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Title: The homogeneous shifts via inductive algebras
Speaker: Prof. M. K. Vemuri Chennai Mathematical Institute Chennai
Date: 20 April 2009
Time: lh -1, department of mathematics indian institute of science, bangalore
Venue: 11.30

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Title: Size biasing with applications to Markov chains and branching processes.
Speaker: K. B. Athreya, Iowa State university
Date: 19 April 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

If X is a positive random variable with a finite mean then the probability distribution with density proprtional to X is called its size biased version. For Markov chains admitting a positive eigen function one can construct a size biased version of this chain which is also Markov.. In this talk we derive conditions for the two chains to be dominated by each other over the full trajectory space.. We then apply this to derive a LLOGL result for supercritical branching processes with arbitrary type space.

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Title: Godunov-type schemes for hyperbolic systems with parameter dependent source; the case of Euler system with friction.
Speaker: Prof. Edwige Godlewski, Laboratoire Jacques-Louis Lions, Universit Pierre et Marie Curie Paris 6
Date: 23 March 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We are interested in deriving schemes having some ‘well-balanced’ and ‘asymptotic preserving’ properties for the approximation of a nonlinear hyperbolic system with source term. In the case of Euler system with friction, the scheme is derived from simple Riemann solvers or equivalently using a relaxation scheme for the enlarged Euler system with ‘potential’. All interested are Welcome

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Title: On a conjecture of Tits and Weiss
Speaker: Prof. Maneesh Thakur, ISI, Delhi
Date: 20 March 2009
Time: 10:00 a.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Tits and Weiss in their book Moufang Polygons have conjectured that the groups of rational points of certain forms of E_6 are generated by some inner transformations. These groups occur as groups of similitudes of certain cubic forms in 27 variables. We will explain this conjecture and report on some results and reductions towards a positive answer.

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Title: On spectrum and arithmetic
Speaker: Prof. C. S. Rajan, TIFR, Mumbai
Date: 20 March 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We will discuss the notion of spectrum and arithmetic of spaces, and expound on the expectation that they should mutually determine each other for the class of locally symmetric spaces associated to congruent arithmetic lattices.

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Title: Size biasing with applications to Markov chains and branching processes.
Speaker: K. B. Athreya, Iowa State university
Date: 19 March 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

If X is a positive random variable with a finite mean then the probability distribution with density proprtional to X is called its size biased version. For Markov chains admitting a positive eigen function one can construct a size biased version of this chain which is also Markov.. In this talk we derive conditions for the two chains to be dominated by each other over the full trajectory space.. We then apply this to derive a LLOGL result for supercritical branching processes with arbitrary type space.

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Title: Assessing copy number variation using genome-wide alignments
Speaker: Dr. Deepayan Sarkar, Fred Hutchinson Cancer Research Institute USA
Date: 02 March 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Polynomial and Rational Hulls
Speaker: Prof. Nikolay Shcherbina Department of Mathematics University of Wuppertal, Germany
Date: 20 February 2009
Time: department of mathematics indian institute of science, bangalore
Venue: 4PM

We will discuss the notions of polynomial and rational convexity. In particular, the question of existence of analytic structure on the additional part of the hull will be considered. Applications of polynomial and rational convexity to other problems of complex analysis will also be given.

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Title: An unusual problem in large deviations
Speaker: S.R.S. Varadhan, Courant Institute
Date: 12 February 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We will investigate the large deviation rates for sums of the form $\sum_i f(x_i) g(x_{2i})$ where $\{x_i\}$ is a nice Markov process. In other words calculate

$\lim_{n\to\infty}{1\over n}\log E[\exp \sum_{i=1}^n f(x_i) g(x_{2i})]$

where $\{x_i\}$ is Markov Chain with transition probability $\pi(x, y)$.

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Title: Recent Trends in Invariant Theory
Speaker: Prof. Roger Howe Mathematics Department, Yale University
Date: 10 February 2009
Time: l h 1, department of mathematics indian institute of science, bangalore
Venue: 04:00pm

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Title: Modulation Spaces and Banach Gelfand Triples
Speaker: Prof. Hans G. Feichtinger University of Vienna, Austria
Date: 19 January 2009
Time: l h i, department of mathematics indian institute of science, bangalore
Venue: 11:15

http://www.univie.ac.at/nuhag-php/scheduler/index.php

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Title: Analysis of the Wright{Fisher Equation
Speaker: Prof. D. W. Stroock M.I.T, USA
Date: 16 January 2009
Time: l h 1, department of mathematics indian institute of science, bangalore
Venue: 4:00

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Title: Homogeneous Vector bundles in Operator theory.
Speaker: Prof. A. Koranyi, Lehman College, CUNY
Date: 15 January 2009
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Support Vector Machines in Machine Learning
Speaker: Hans D. Mittelmann (Department of Math & Stats, Arizona State University)
Date: 06 January 2009
Time: department of mathematics indian institute of science, bangalore
Venue: 02:30

Very large datasets occur in the area of machine learning (ML). The tasks are having a computer “learn” to read handwriting, to understand speech, to recognize faces, to filter spam e-mail etc. Mathematically, these problems lead to huge optimization problems, of an, however not unfavorable type, namely convex quadratic programs (QP).

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Title: Optimization Software for Financial Mathematics
Speaker: Hans D. Mittelmann (Department of Math & Stats, Arizona State University)
Date: 05 January 2009
Time: department of mathematics indian institute of science, bangalore
Venue: 02:30

Information about available software to solve a large variety of optimization problems is provided at plato.asu.edu/guide.html while some of this software is evaluated at plato.asu.edu/bench.html. Starting with these sources an overview will be given on codes that are particularly useful for applications in mathematical finance.

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Title: Stochastic Lagrangian Particle systems for the Navier-Stokes and Burgers equations.
Speaker: Dr. Gautam Iyer, Stanford University
Date: 02 January 2009
Time: 2:30 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

I will introduce an exact stochastic representation for certain non-linear transport equations (e.g. 3D-Navier-Stokes, Burgers) based on noisy Lagrangian paths, and use this to construct a (stochastic) particle system for the Navier-Stokes equations. On any fixed time interval, this particle system converges to the Navier-Stokes equations as the number of particles goes to infinity.

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Title: Comparitive description of Circuits in Classical and Quantum Computers
Speaker: Prof. K. R. Parthasarathy Indian Statistical Institute, Delhi
Date: 30 December 2008
Time: l h 1, department of mathematics indian institute of science, bangalore
Venue: 11:15

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Title: KRS bases for rings of invariants
Speaker: Dr. K. N. Raghavan, I.M.Sc.
Date: 26 December 2008
Time: 2:30 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

The talk will be a report on an ongoing research project (joint with Preena Samuel and K.V.Subrahmanyam). Representation theoretic consequences will be worked out of the combinatorial characterizations of left, right, and two-sided Kazhdan-Lusztig cells of the symmetric group. Applications to invariant theory and both ordinary and modular representation theory of the symmetric group will be given.

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Title: Complex Interpolation for Banach Spaces of Operators
Speaker: Prof. G. Pisier University Of Paris 6 and Texas A & M University
Date: 24 December 2008
Time: department of mathematics indian institute of science, bangalore
Venue: 11:15

http://math.iisc.ernet.in/~imi/downloads/gpisier.pdf

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Title: Approximation of currents and applications to complex geometry
Speaker: Prof. J. Demailly Institnt Fourier France
Date: 23 December 2008
Time:
Venue:

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Title: Infinitesimal Hecke algebras
Speaker: Dr. Apoorva Khare, U.C. Riverside
Date: 17 December 2008
Time: 11.00 a.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We study families of infinite-dimensional algebras that are similar to semisimple Lie algebras as well as symplectic reflection algebras. Infinitesimal Hecke algebras are deformations of semidirect product Lie algebras, and we study two families over $\mathfrak{sl}(2)$ and $\mathfrak{gl}(2)$. Both of them have a triangular decomposition and a nontrivial center, which allows us to define and study the BGG Category $\mathcal{O}$ over them - including a (central character) block decomposition, and an analog of Duflo’s Theorem about primitive ideals. We then discuss certain related setups.

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Title: Dirichlet Processes and Reflected Diffusions
Speaker: Dr. Kavita Ramanan, Carnegie Mellon University
Date: 16 December 2008
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Reflected diffusions arise in many contexts. We identify a rather general condition under which these diffusions belong to the class of so-called Dirichlet processes, which are a generalization of continuous semimartingales that admit many nice properties, including an Ito formula. We also provide an example arising from applications, in which the reflected diffusion fails to be a semimartingale, but belongs to the class of Dirichlet processes. This is partly based on joint work with Weining Kang.

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Title: The Embedded Contact Homology of Circle Bundles over Riemann Surfaces
Speaker: Dr. David Farris, U.C. Berkeley
Date: 16 December 2008
Time: 11.30 a.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Embedded contact homology (ECH) is an invariant of three-manifolds due to Hutchings, Sullivan, and Taubes. It uses a contact structure on a three-manifold to produce an invariant of the underlying topological manifold. The invariant is the homology of a chain complex generated by certain closed orbits of the Reeb vector field (of interest in classical dynamics), whose differential counts certain holomorphic curves in the symplectization of the contact three-manifold. Few nontrivial examples of ECH have been computed. In this talk, I will give some background and context on ECH and then describe the computation of the ECH of circle bundles over Riemann surfaces, in which the relevant holomorphic curves are actually meromorphic sections of complex line bundles.

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Title: Temporal spike pattern learning in biological systems
Speaker: Dr. Sachin S. Talathi (University of Florida, Gainesville, USA)
Date: 14 November 2008
Time: department of mathematics indian institute of science, bangalore
Venue: 4pm

The central question will be focused around the design and implementation of neuronal circuitry involved in the task of decoding sensory information. Sensory information is encoded in the form of sequence of action potential spikes by the peripheral nervous system. This information is then passed onto the central nervous system (CNS) to generate an appropriate response. The action potential spikes are identical in shape and therefore it is assumed that all the information about the environment is embedded in the timing of occurrences of these spikes. The question then is, what neural architecture exists in the CNS to decode this information?

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Title: Complex dimensions, attached analytic discs and parametric argument principle
Speaker: Mark Agranovsky, Bar-Ilan University
Date: 19 September 2008
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Complex dimensions, attached analytic discs and parametric argument principle
Speaker: Mark Agranovsky, Bar-Ilan University
Date: 12 September 2008
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Conservation laws admitting delta shock wave type solutions
Speaker: Prof. Prof. G. D. Veerappa Gowda TIFR-CAM, Bangalore
Date: 29 August 2008
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Noncommutative geometry and mirror symmetry
Speaker: Dr. Pranav Pandit University of Pennsylvania
Date: 25 August 2008
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

I will outline an approach to noncommutative geometry, due largely to M. Kontsevich, where certain A-infinity categories play the role of spaces. This noncommutative geometry program draws much of its inspiration from homological mirror symmetry. The talk will be purely expository: it will not contain any new results.

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Title: Some uncertainty principles on solvable Lie groups
Speaker: Prof. Ali Baklouti Department of Mathematics, University of Sfax, Sfax, Tunisia
Date: 22 August 2008
Time: department of mathematics indian institute of science, bangalore
Venue: L

The aim of this series of lectures is to seek analogies of some known uncertainty principles, proved in the case of the real line to certain solvable Lie groups. We will speak about uncertainty principles of Hardy, Cowling Price, Morgan and Beurling and present some recent results on their non commutative analogues. Furthermore, we will also talk about sharpness of the decay condition in Hardys principle and give some new result in that context.

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Title: Inconsistency of the Bootstrap in Problems Exhibiting Cube Root Asymptotics
Speaker: Dr. Moulinath Banerjee University of Michigan
Date: 13 August 2008
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate $n^{1\\over 3}$. The Grenander estimator, the nonparametric maximum likelihood estimator of an unknown non-increasing density function $f$ on $[0,\\infty)$, is a prototypical example. We focus on this example and explore different approaches to constructing bootstrap confidence intervals for $f(t_0)$, where $t_0 \\in (0,\\infty)$ is an interior point. We find that the bootstrap estimate, when generating bootstrap samples from the empirical distribution function or its least concave majorant, does not have any weak limit in probability. Bootstrapping from a smoothed version of the least concave majorant, however, leads to strongly consistent estimators and the $m$ out of $n$ bootstrap method is also consistent. Our results cast serious doubt on some previous claims about bootstrap consistency (in the class of cube root problems) in the published literature.

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Title: Estimation of function thresholds using multistage adaptive procedures
Speaker: Dr. Moulinath Banerjee University of Michigan
Date: 12 August 2008
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

In this talk, I will discuss threshold estimation for a regression function in some different settings. The threshold can either be a change–point, i.e. a point of jump discontinuity in an otherwise smooth curve, or the first time that a regression function crosses a certain level. Both problems have numerous applications in a variety of spheres, like biology (pharmacology, dose-response experiments) and engineering. Our goal is to estimate thresholds of this type given a fixed budget of points to sample from, but with the flexibility that batch sampling can be done in several stages, so that adaptive strategies are possible. Our strategy is to use multistage zoom-in procedures to estimate the threshold: an initial fraction of the sample is invested top come up with a first guess, an adequate neighborhood of the first guess is chosen, more points are sampled from this neighborhood and the initial estimate id updated. The procedure continues thus, ending in a finite number of stages. Such zoom-in procedures result in accelerated convergence rates over any one–stage method. Approximations to relative efficiencies are computed and optimal allocation strategies, as well as recipes for construction of confidence sets discussed.

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Title: Preferential Attachment Random graphs with general weight function and general input sequence.
Speaker: Dr. K. B. Athreya Iowa State University
Date: 04 August 2008
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Consider a network of sites growing over time such that at step n a newcomer chooses a vertex from the existing vertices with probability proportional to a function of the degree of that vertex, i.e., the number of other vertices that this vertex is connected to. This is called a preferential attachment random graph. The objects of interest are the growth rates for the growth of the degree for each vertex with n and the behavior of the empirical distribution of the degrees. In this talk we will consider three cases: the weight function w(.) is superlinear, linear, and sublinear. Using recently obtained limit theorems for the growth rates of a pure birth continuous time Markov chains and an embedding of the discrete time graph sequence in a sequence of continuous time pure birth Markov chains, we establish a number of results for all the three cases. We show that the much discussed power law growth of the degrees and the power law decay of the limiting degree distribution hold only in the linear case, i.e., when w(.) is linear.We also discuss the case of arbitrary input sequence.

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Title: Conformal invariance in probability and statistical physics
Speaker: Dr. Manjunath Krishnapur University of Toronto
Date: 29 July 2008
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

This is an expository talk whose aim will be to give an introduction to SLE (Schramm-Loewner evolution), discovered by Oded Schramm in 2000 to describe many critical statistical mechanical systems.

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Title: Modular Forms, Elliptic Curves and Galois Representations.
Speaker: Dr. Aftab Pande Cornell University
Date: 23 July 2008
Time: 4.00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

I will give a brief overview of Wiles’ proof of Fermat’s Last Theorem, and explain the connection between modular forms and elliptic curves via Galois representations e.g. the Taniyama-Shimura conjecture. In the second half, I’ll explain some recent results on p-adic modular forms and deformations of Galois representations. If time permits, I’ll outline a future project on ranks of elliptic curves.

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Title: Lattice Point Asymptotics and Volume Growth on Teichmuller space
Speaker: Dr. Jayadev Athreya Department of Mathematics, Yale University
Date: 16 July 2008
Time: 11.30 a.m.
Venue: Lecture Hall - III, Dept. of Mathematics

We apply some of the ideas of the Ph.D. Thesis of G. A. Margulis to Teichmuller space. Let x be a point in Teichmuller space, and let B_R(x) be the ball of radius R centered at x (with distances measured in the Teichmuller metric). We obtain asymptotic formulas as R tends to infinity for the volume of B_R(x), and also for for the cardinality of the intersection of B_R(x) with an orbit of the mapping class group.

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Title: Lattice Point Asymptotics and Volume Growth on Teichmuller space
Speaker: Dr. Jayadev Athreya Department of Mathematics, Yale University
Date: 11 July 2008
Time: 4.00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

We apply some of the ideas of the Ph.D. Thesis of G. A. Margulis to Teichmuller space. Let x be a point in Teichmuller space, and let B_R(x) be the ball of radius R centered at x (with distances measured in the Teichmuller metric). We obtain asymptotic formulas as R tends to infinity for the volume of B_R(x), and also for for the cardinality of the intersection of B_R(x) with an orbit of the mapping class group.

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Title: The Gorenstein Colength of an Artinian Local Ring
Speaker: Ananth Hariharan
Date: 24 June 2008
Time: 4:00 p.m.
Venue: LH 1, Mathematics Department

The question we are interested in is the following: Given an Artinian local ring, how ‘close’ can we get to it by an Artinian Gorenstein local ring. In this talk I will make the notion of being ‘close’ precise numerically. We will exhibit some natural bounds on this number and discuss some (old and new) results. In particular, if R is a quotient of a power series ring over a field of characteristic zero by a power of the maximal ideal, we will see how one can compute this number.

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Title: Eigencurve methods for some generalised eigenvalue problems
Speaker: Professor Paul Binding, Department of Mathematics, University of Calgary, Canada
Date: 23 May 2008
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Many applied problems give rise to generalised eigenvalue problems of the form Ay = s By, where A and B are operators of various possible types, and s is an eigenparameter. Two parameter embeddings Ay = s By - t Cy generate useful methods of attack, and can be traced back about a century, but new applications are still appearing. They provide ways to visualise simply some quite complicated phenomena, and in this talk I will discuss some older and newer ones that I have found interesting.

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Title: The MOR cryptoystem and special linear groups over finite fields
Speaker: Dr. Ayan Mahalanobis, Stevens institute, New Jersey
Date: 21 May 2008
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

The ElGamal cryptosystem is in the heart of public key cryptography. It is known that the MOR cryptosysetm generalizes it from the cyclic group to the automorphism group of a (non-abelian) group. I will start by describing the MOR cryptosystem and then we will use the special linear group over a finite field as the platform group. It seems likely that this project is competitive with the elliptic curves over finite fields in terms of security. I’ll explain why I think so. Then we can talk about challenges in implementation of this cryptosystem. All interested are Welcome

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Title: Null controllability of a fluid-structure model
Speaker: Professor Jean-Pierre Raymond
Date: 25 February 2008
Time: 4.00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

We consider a system coupling the Stokes system with an elastic structure modelled by a finite dimensional system. We prove that this system can be driven to zero by a control action only in the fluid equation. The proof is based on a global Carleman inequality. Because of the coupling between the fluid equation and the structure new boundary terms appear in the Carleman inequality, and estimating these terms requires new techniques.

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Title: 3-D Kinematical Conservation Laws: equations of evolution of a surface
Speaker: Prof. Phoolan Prasad
Date: 22 February 2008
Venue: Lecture Hall 3, Department of Mathematics

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Title: MATHEMATICAL MODELLING IN HEMODYNAMICS I
Speaker: Dr. Anna Zau=9Akov=E1 Institute of Numerical Simulation, Hamburg University of Technology, Germany
Date: 15 February 2008
Venue: LH-1 , Math Dept

2D Mathematical model an numerical simulations of non-Newtonian shear depen= dent=20 flow with fluid-structure interaction

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Title: Watson-Crick pairing for RNA and Milnor's link invariants
Speaker: Dr. Siddhartha Gadgil, IISc
Date: 06 February 2008
Time: 4:00 p. m.
Venue: Lecture Hall III, Dept. of Mathematics

We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which can be interpreted in terms of the Heisenberg group as well as lattice paths, which we call the Heisenberg invariant.

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Title: Lorenz knots and modular knots.
Speaker: P. Dehornoy.
Date: 04 February 2008
Time: 4-5 pm
Venue: LH 1, IISc Maths Dept

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Title: Watson-Crick pairing for RNA and Milnor's link invariants
Speaker: Dr. Siddhartha Gadgil, IISc
Date: 22 January 2008
Time: 4:00 p. m.
Venue: Lecture Hall III, Dept. of Mathematics

We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which can be interpreted in terms of the Heisenberg group as well as lattice paths, which we call the Heisenberg invariant.

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Title: Mathematical Aspects of 2-dimensional Yang-Mills Theory
Speaker: Prof. Ambar Sengupta Louisiana State University.
Date: 18 January 2008
Time: 4.00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

Yang-Mills gauge theory, classical as well as quantum, in two dimensions is both mathematically tractable and poses interesting questions. The quantum theory for the field has a mathematically precise formulation in terms of a Gaussian measure. Classical holonomies become group-valued random variables in this setting. This talk will present an overview of some mathematical problems, solutions, and ideas arising from two-dimensional Yang-Mills theory

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Title: Graph Spectra: A Tool for Analyzing Networks
Speaker: Dr. D. Anirban Banerjee, Max-Planck Institute, Leipzig
Date: 17 January 2008
Time: 4.15 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

The existing graph invariants can retrieve certain structural informations, but they are not sufficient to capture all qualitative aspects of a graph. One of the aim of graph theory to identify on one hand the unique and special feature for the network from a particular class and on the other hand the universal qualities that are shared by other network structures. It is a challenge to specify the domain of a given a network structure, on the basis of certain unique qualitative features. We develop theoretical scheme and apply the general method, based on the spectral plot of the normalized graph Laplacian, that is easily visually analyzed and can be considered as excellent diagnostic to categorize the networks from different sources. Construction with different graph operation related to evolution of a network produce specific eigenvalue, describe certain processes of graph formation that leave characteristic traces in the spectrum. We show how useful plausible hypothesis about evolutionary process can be made by investigating the spectra of a graph constructed from actual data. Based on this idea we have reconstructed protein-protein interaction network which is structurally more close to real protein-protein interaction networks than the networks constructed by other models. We also introduced a tentative classification scheme for empirical networks based on global qualitative properties detected through the spectrum of the Laplacian of the graph underlying the network.This method identifies several distinct types of networks across different domains of applications, which is rather difficult by other existing tool and parameters. Thus we infer that spectral distribution is complete qualitative characterization of a graph.

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Title: Hochschild homology of rings of differential operators and integration over complex manifolds.
Speaker: Dr. D. Ajay Ramadoss, University of Oklahoma.
Date: 08 January 2008
Time: 4.00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

Let X be a compact complex manifold and let E be a holomorphic vector bundle on X. Any global holomorphic differential operator D on E induces an endomorphism of $\\text{H}^{\\bullet}(X,E)$. The super-trace of this endomorphism is the super-trace of D. This is a linear functional on the 0-th Hochschild homology of Diff(E), the algebra of global holomorphic differential operators on E. While the Hochschild homology in the usual sense of Diff(E) is too big for explicit computation, there is a notion of completed Hochschild homology of Diff(E) with a very nice property: If HH_i(Diff(E)) denotes the i-th completed Hochschild homology, then HH_i(Diff(E)) is isomorphic to \\text{H}^{2n-i}(X), the 2n-i th cohomology of X with complex coefficients. We shall attempt to outline how the supertrace mentioned above extends to a linear functional on the 0-th completed Hochschild homology of Diff(E), and thus, on H^{2n}(X). A priori, this linear functional depends on E. It however, can be shown that it is precisely the integral over X. This fact also helps one connect the local Riemann-Roch theorems of Nest-Tsygan to the Hirzebruch Riemann-Roch theorem. Analogous results about similar constructions using cyclic homology instead of Hochschild homology are also available.

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Title: Directionally convex ordering of random measures, shot-noise fields and some applications to wireless networks.
Speaker: Dr. D. Yogeshwaran, Ecole Normale Superieure, Paris.
Date: 04 January 2008
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

In the standard stochastic geometric setting, wireless networks can be modeled as point processes and their performances as certain mean functionals of the point process. Obtaining closed form expressions of such functionals is not easy for a general class of point processes. This motivates a comparative study. We study comparison of one such class of mean functionals - the additive and extremal shot-noise fields - which arise naturally in modeling of wireless networks, as ingredients of the so called Signal-to-Interference-Noise-Ratio.

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Title: Holomorphic extension of CR functions from hypersurfaces with singularities
Speaker: Dr. Debraj Chakrabarti, University of Western Ontario
Date: 20 December 2007
Time: 11.30 a.m.
Venue: Lecture Hall - III, Dept. of Mathematics

We show that Trepreau’s theorem (minimality of a hypersurface at a point implies one sided extension of all CR functions) does not hold if the hypersurface is allowed to have singularities. We formulate a geometric condition called two sided support which is the obstruction to such extension.

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Title: The Hodge Conjecture for certain abelian four-folds: a tentative gauge theoretic approach.
Speaker: Prof. T. R. Ramadas, ICTP, Trieste
Date: 18 December 2007
Time: 2.00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

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Title: The Newton Polygon
Speaker: Prof. Sriram Abhyankar, Purdue Universtiy
Date: 14 December 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Ergodic theory, abelian groups, and point processes associated with stable random fields
Speaker: Dr. Parthanil Roy, ETH Zurich and Michigan State University
Date: 10 December 2007
Time: 10.00 a.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We consider a point process sequence induced by a stationary symmetric -stable (0 < < 2) discrete parameter random eld. It is easy to prove, following the arguments in the one-dimensional case in Resnick and Samorodnitsky (2004), that if the random eld is generated by a dissipative group action then the point process sequence converges weakly to a cluster Poisson process. For the conservative case, no general result is known even in the one-dimensional case. We look at a specic class of stable random elds generated by conservative actions whose eective dimensions can be computed using the structure theorem of nitely generated abelian groups. The corresponding point processes sequence is not tight and hence needs to be properly normalized in order to ensure weak convergence. This weak limit is computed using extreme value theory and some counting techniques. (This talk is based on a joint work with Gennady Samorodnitsky) All interested are Welcome

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Title: Some queer diffusions
Speaker: Prof. Daniel Stroock, MIT
Date: 07 December 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Least area surfaces are incompressible
Speaker: Dr. Siddhartha Gadgil, IISc
Date: 06 December 2007
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Least area surfaces are incompressible
Speaker: Dr. Siddhartha Gadgil, IISc
Date: 05 December 2007
Time: 4:00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Domains with non-compact automorphism group
Speaker: Dr. Kaushal Verma, IISc
Date: 30 November 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

The purpose of the talk will be to discuss the problem about classifying domains in C^n that have a non-compact group of holomorphic automorphisms. Examples and a flavour of some of the techniques that have been successful so far will be provided.

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Title: Linear and integer programming: The state of the art
Speaker: Prof. Martin Groetschel (Institut fur Mathematik, Technische Universitt Berlin)
Date: 28 November 2007
Time: 4:00 pm
Venue: Faculty Hall

In this lecture I will survey - aimed at a broad mathematical audience - the development of linear and integer programming. The history of these subjects began about one and a half centuries ago but their “boom” started in the 1950s only. Theory, algorithm design and analysis dominated the first years of development. Computational progress was particularly significant in the last twenty years. In fact, the advances in linear and integer programming software are on at least the same level as those in computing machinery.

These achievements combined with successful efforts to model applications make it possible to solve today real world problems of breath taking size and diversity. I will report about some of these success stories in my talk.

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Title: Galois action on L-values
Speaker: Dr. N. Tejaswi, IISc
Date: 23 November 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

To an elliptic curve E, one can associate various twists L(E,\\chi,s) of L-functions. The values of these L-functions at integers are expected to behave well under the action of a Galois group. In this talk, we will explain how a Galois group acts on some special L-values and indicate some approaches in studying the behaviour under such actions.

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Title: Spectral Pick interpolation from a complex-geometric viewpoint
Speaker: Dr. Gautam Bharali
Date: 16 November 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

The spectral Pick-interpolation problem, i.e. to determine when there exists a holomorphic map from the unit disc to the class of complex matrices of spectral radius less than one that interpolates prescribed data, has a complicated solution using operator-theory and control-theory methods. The difficulty in implementing this solution motivated a new approach pioneered by Agler and Young. Their methods led to a checkable necessary condition for Pick interpolation. But, from a complex-geometric viewpoint, it was unclear why the latter condition should be sufficient. In this talk, we will demonstrate that this condition is not sufficient. We will also present an inequality – largely linear-algebraic in flavour – that provides a necessary condition for matricial data for which the Agler-Young-type test provides no conclusions.

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Title: Chern-Cheeger-Simons theory of secondary classes
Speaker: Dr. Jaya Iyer, IMSc.
Date: 13 November 2007
Time: 2.00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

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Title: Cycles on complete intersections
Speaker: Dr. Jaya Iyer, IMSc.
Date: 12 November 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We discuss some questions on the triviality of rational Chow groups and give some examples in this direction.

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Title: Ergodic theory, abelian groups, and point processes associated with stable random fields
Speaker: Dr. Parthanil Roy, ETH Zurich and Michigan State University
Date: 10 November 2007
Time: 10.00 a.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We consider a point process sequence induced by a stationary symmetric -stable (0 < < 2) discrete parameter random eld. It is easy to prove, following the arguments in the one-dimensional case in Resnick and Samorodnitsky (2004), that if the random eld is generated by a dissipative group action then the point process sequence converges weakly to a cluster Poisson process. For the conservative case, no general result is known even in the one-dimensional case. We look at a specic class of stable random elds generated by conservative actions whose eective dimensions can be computed using the structure theorem of nitely generated abelian groups. The corresponding point processes sequence is not tight and hence needs to be properly normalized in order to ensure weak convergence. This weak limit is computed using extreme value theory and some counting techniques. (This talk is based on a joint work with Gennady Samorodnitsky) All interested are Welcome

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Title: History of irrational and transcendental numbers
Speaker: Prof. Michel Waldschmidt, Institut de Mathmatiques de Jussieu, Paris
Date: 06 November 2007
Time: 2.00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

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Title: Negatively curved Kahler manifolds
Speaker: Martin Deraux (Institut Fourier, Grenoble)
Date: 31 October 2007

Lecture Series on “ Negatively curved Kahler manifolds” (4 Lectures)

Speaker: Dr. Martin Deraux, Institut Fourier, Grenoble

Time and place: LH 2, IISc Math Dept

Abstract:

  1. Basics of Kahler geometry, uniformization.
  2. Intro to complex hyperbolic geometry, review about symmetric spaces, constructions of discrete groups and lattices, Calabi conjecture and Yau uniformization.
  3. Overview of Deligne-Mostow theory.
  4. Branched covering constructions and non-locally symmetric examples.

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Title: Non-negative isotropic curvature
Speaker: Dr. Harish Seshadri, IISc
Date: 26 October 2007
Time: 4.00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

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Title: Quantum Cryptography, Mutually Unbiased Basis and what is wrong with Classical Cryptography
Speaker: Professor Asha Rao, RMIT, Melbourne, Australia
Date: 28 September 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Starting with a brief description of classical cryptography and the need for quantum cryptography, I will elaborate on some of the mathematical questions within quantum cryptography, ending with the details on a a particular problem - the construction of mutually unbiased basis.

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Title: Quantum field theory as an aid to geometers Finite Element Methods
Speaker: Professor Dr. Katrin Wendland Univ. Augsburg, Germany
Date: 24 September 2007
Time: 10.00 a.m.
Venue: Lecture Hall - II, Dept. of Mathematics

String theorists believe that elementary particles can be described by one dimensional string-like objects that propagate in certain geometries. An appropriate mathematical treatment combines the study of quantum field theory and geometry. Whether or not one believes in the physical (or even mathematical) reality of string theory as a whole, the idea to use one-dimensional test particles to investigate the properties of interesting geometries allows far reaching insights- both in quantum field theory and in geometry.

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Title: Some Remarks on the Convergence of Adaptive Finite Element Methods
Speaker: Professor Dr. Carsten Carstensen Humboldt Univ., Germany
Date: 24 September 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Typical adaptive mesh-refining algorithms for first-oder (conforming) finite element methods consist of a sequence of the following steps:

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Title: Combinatorial approach to the conjugacy-class algebra of the symmetric group
Speaker: Prof. Jacob Katriel, Technion - Israel Institute of Technology, Haifa
Date: 14 September 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

For A=(1)^{l_1}(2)^{l_2}…(n)^{l_n} a conjugacy class in S_n, let

Supp(A)=\\Sum_{i=1}^n i\\cdot l_i=n-l_1

Evaluation of the coefficient of the calss-sum C in the product of the class sums A and B is reduced to a combinatorial problem in S_k, where k=min{Supp(A),Supp(B),Supp(C)}

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Title: Multivariate Distributions, Quantiles and their Monotonicity Properties.
Speaker: Prof. Probal Chaudhari, ISI, Kolkata.
Date: 07 September 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Some notions of multivariate distribution transform and related quantile transform will be introduced and discussed. Some application of these statistical concepts and tools in social and natural sciences will be described.

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Title: Some Combinatorial Group Invariants and their genaralisations with weights
Speaker: Prof. S.D. Adhikari, HRI, Allahabad,
Date: 05 September 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Overconvergent modular symbols
Speaker: Dr. B. Baskar, Brandeis University,
Date: 31 August 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

The notion of modular symbols was first introduced by Manin. We state some basic results which relate modular symbols to special values of L-functions and p-adic L-functions. We give Greenberg and Stevens construction of an overconvergent modular symbols which is a measure valued cohomology class attached to a Hida family of modular forms with certain interpolation properties. We will construct the Mazur-Kitagawa two variable p-adic L-function from the overconvergent modular symbol.

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Title: On the numerical approximation of nonconservative hyperbolic balance laws
Speaker: Dr. Marcus Kraft Hamburg University of Technology, Germany
Date: 10 August 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Hyperbolic balance laws with source terms allow non-unique entropy solutions. By taking the source term as a variable and stating its time derivative to be zero, a balance law can be rewritten in a quasi-linear form. This then reveals the loss of strict hyperbolicity at critical states, the so called resonance phenomenon. Numerical schemes are sensitive to this phenomenon and it is uncertain, which entropy solution (if it is non-unique) will be created by an appropriate numerical scheme.

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Title: Classification problems in topology - some approaches
Speaker: Prof. Himadri Mukherjee North-Eastern Hill University, Shillong
Date: 02 August 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: The arithmetic of elliptic surfaces
Speaker: Dr. Ritabrata Munshi, Rutgers University, USA
Date: 01 August 2007
Time: 2.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

A family of elliptic curves (or an elliptic surface) is given by a Weierstrass equation

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Title: The arithmetic of elliptic surfaces
Speaker: Dr. Ritabrata Munshi, Rutgers University, USA
Date: 31 July 2007
Time: 11.30 a.m.
Venue: Lecture Hall - I, Dept. of Mathematics

A family of elliptic curves (or an elliptic surface) is given by a Weierstrass equation

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Title: On holomorphic Hermitian Bundles
Speaker: Prof. Indranil Biswas, TIFR, Mumbai
Date: 27 July 2007
Time: 4.00 p.m.
Venue: Lecture Hall - III, Dept. of Mathematics

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Title: Spectral Theory and Root bases associated with Multiparameter Eigenvalue Problems
Speaker: Mr. J. P. Mohan Das Ph. D. Research Scholar Department of Mathematics
Date: 26 July 2007
Time: 11.00 a.m.
Venue: Lecture Hall III, Department of Mathematics

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Title: On a scaling limit for a tagged particle in some zero-range interacting systems
Speaker: Dr. Sunder Sethuraman, Iowa State University
Date: 29 June 2007
Time: 3.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Informally, the zero-range'' particle system follows a collection of dependent random walks on a lattice, each of which interacts infinitesimally only with those particles already present at its location. In this talk, we consider the asymptotics of a distinguished, or tagged particle in this interacting particle system. In particular, we discuss anonequilibrium’’ invariance principle, in one dimension when the transition rates are mean-zero, with respect to a diffusion whose coefficients depend on the ``hydrodynamic’’ density.

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Title: Multiplicity Conjecures
Speaker: Dr. Manoj Kummini, University of Kansas
Date: 28 June 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We discuss a conjecture for the Hilbert-Samuel multiplicity (degree) of a homogeneous ideal in a polynomial ring over a field. Herzog-Huneke-Srinivasan conjectured that the multiplicity can be bounded by a function of the maximum twists occuring at different homological degrees in a minimal graded free resolution of the ideal. We will discuss some examples and some cases where the conjecture is known to hold.

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Title: Lipschitz isomorphisms between Banach spaces
Speaker: Prof. G. Godefroy University of Paris VI France
Date: 19 June 2007
Time: 4:00 p.m.
Venue: Lecture Hall -I, Dept. of Mathematics

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Title: Harmonic analysis approach to the Navier-Stokes equation
Speaker: Prof. S. S. Sritharan, University of Wyoming
Date: 15 June 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: An overview of random matrices
Speaker: Dr. Manjunath Krishnapur, University of Toronto
Date: 14 June 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

We consider the simplest models of Hermitian and non Hermitian random matrices with independent and identically distributed entries. We present basic results on limiting spectral distributions (Wigner’s semicircle law in the Hermitian case and Girko’s circular law in the non Hermitian case).

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Title: Higher linking of Knots: Stallings theorem
Speaker: Ms. Geetanjali Kachari, IISc
Date: 11 June 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

A central result used in studying higher linking of knots is a theorem of Stalling on lower central series. Stallings’s proof was based on spectral sequences, but he indicated that the result can be proved directly using Hopf’s description of homology of groups. In this talk Stallings theorem will be explained and a direct proof will be presented.

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Title: Adaptive Numerical Solution of Intracellular Calcium Dynamics
Speaker: Prof. Gerald Warnecke, Magdeburg, Germany
Date: 21 May 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Calcium waves are an important means of intrcellular signaling. Intracellular calcium release at the endoplasmatic reticulum is a prime example of the role of stochastic effects in cellular systems. Realistic models consist of deterministic systems of reaction-diffusion equations in three dimensional space coupled to stochastic transitions of calcium channels at the domain boundary. The resulting dynamics has multiple time and space scales, which complicates computer simulations. In this talk we focus on the PDE aspect of the numerical computations. We use adaptive linear finite elements to efficiently resolve the extreme spatial gradients of concentration variables close to a channel. Further, parallel computing is needed for realistic simulations. We describe the algorithmic approach and we demonstrate its efficiency by computational examples. Our single channel model matches experimental data by Mak et al. (PNAS 95, 1998) and results in intriguing dynamics if calcium is used as a carrier. Random openings of the channel accumulate in bursts of calcium blips that may prove central for the understanding of cellular calcium dynamics. We plan to extend our computations to more realistic domain geometries and to use local time stepping methods.

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Title: Numerical approximation of population balance equations in process engineering
Speaker: Prof. Gerald Warnecke, Magdeburg, Germany
Date: 14 May 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

Population balance equations are widely used in many chemical and particle process engineering problems involving crystallization, fluidized bed granulation, aerosols etc. Analytical solutions are available only for a limited number of simplified problems and therefore numerical solutions are frequently needed to solve a population balance problem. A general population balance equation for simultaneous aggregation, breakage, growth and nucleation in a well mixed system is given as an integro-partial differential equation for a particle property distribution function. Sectional methods are well known for their simplicity and conservation properties. Therefore numerical techniques belonging to this category are the most commonly used. In these methods, all particles within a computational cell, which in some papers is called a class, section or interval, are supposed to be of the same size. These methods divide the size range into small cells and then apply a balance equation for each cell. The continuous population balance equation is then reduced to a set of ordinary differential equations. However, it is well known that the numerical results by previous sectional methods were rather inaccurate. Furthermore, there is a lack of numerical schemes in the literature which can be used to solve growth, nucleation, aggregation, and breakage processes, i.e. differential and integral terms, simultaneously. We present a new numerical scheme for solving a general population balance equation which assigns particles within the cells more precisely. The technique follows a two step strategy. The first is to calculate the average size of newborn particles in a cell and the other to assign them to neighboring nodes such that important properties of interest are exactly preserved. The new technique preserves all the advantages of conventional discretized methods and provides a significant improvement in predicting the particle size distributions. The technique allows the convenience of using geometric- or equal-size cells. The numerical results show the ability of the new technique to predict very well the time evolution of the second moment as well as the complete particle size distribution. Moreover, a special way of coupling the different processes has been described. It has been demonstrated that the new coupling makes the technique more useful by being not only more accurate but also computationally less expensive. Furthermore, a new idea that considers the growth process as aggregation of existing particle with new small nuclei has been presented. In that way the resulting discretization of the growth process becomes very simple and consistent with first two moments. Additionally, it becomes easy to combine the growth discretization with other processes. Moreover all discretizations including the growth have been made consistent with first two moments. The new discretization of growth is a little diffusive but it predicts the first two moments exactly without any computational difficulties like appearance of negative values or instability etc. The accuracy of the scheme has been assessed partially by numerical analysis and by comparing analytical and numerical solutions of test problems. The numerical results are in excellent agreement with the analytical results and show the ability to predict higher moments very precisely. Additionally, an extension of the proposed technique to higher dimensional problems is discussed

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Title: Higher linking of knots.
Speaker: Dr. Siddhartha Gadgil, IISc
Date: 09 May 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

This will be an informal expository talk on higher linking of knots in three-dimensional space.

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Title: Local polynomial convexity of real surfaces in C^n near complex tangencies
Speaker: Dr. Gautam Bharali, IISc
Date: 13 April 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

More than 30 years after the Harvey-Wells paper on complex approximation theory, we still do not know the answers to most of the relevant approximation-theoretic questions on, say, a smooth, compact 2-manifold (call it M) in C^2. Answering many of these questions boils down to examining the local polynomial convexity of M near those points where the (extrinsic) tangent space of M is a complex subspace of the ambient C^2. We shall quickly survey what is currently known, and then look at some recent progress based on examining the Maslov index.

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Title: Projective modules over affine algebras
Speaker: Dr. Mrinal Kanti Das, Indian Statistical Institute, Kolkata
Date: 02 April 2007
Time: 10.00 a.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: How interesting are orbifolds?
Speaker: Mainak Poddar ISI Kolkata
Date: 23 March 2007
Time: 4:00 p.m.
Venue: Lecture Hall - I, Department of Mathematics

Orbifolds are generally regarded as generalizations of manifolds. On the other hand, finite groups are also orbifolds. In this survey talk, I will focus on how orbifolds appear naturally in some important areas of Mathematics and Physics. I will also describe some features of the geometry of orbifolds.

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Title: Numerical Modeling of Hyperbolic Balance Laws using Bicharacteristics
Speaker: Prof. M. Lukacova, Hamburg University of Technology
Date: 14 March 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Numerical Modeling of Hyperbolic Balance Laws using Bicharacteristics
Speaker: Prof. M. Lukacova, Hamburg University of Technology
Date: 13 March 2007
Time: 4.00 p.m.
Venue: Lecture Hall - II, Dept. of Mathematics

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Title: Zariski-Lipman Conjecture
Speaker: Prof. Dilip Patil, IISc
Date: 08 March 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

In this lecture I will give a brief survey on the well-known Zariski-Lipman Conjecture which is still open in general. However, there are some partial results have been proved. I will state these results by giving necessary definitions and concepts required.

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Title: Mathematical issues for some control problems in fluid mechanics
Speaker: Prof. Jean-Pierre Raymond Universit Paul Sabatier, Toulouse, France HRI, Allahabad
Date: 28 February 2007
Time: 4.00 p.m.
Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Real vs. Strongly Real Elements in Algebraic Groups
Speaker: Dr. Anupam Kumar Singh, TIFR, Mumbai
Date: 27 February 2007
Time: 4.00 p.m.
Venue: Lecture Hall - II, Dept. of Mathematics

Let $k$ be a field of characteristic not 2 and $G$ be an algebraic group defined over $k$. An element $t$ in $G(k)$ is called real if there exists $g \in G(k)$ such that $gtg^{-1}=t^{-1}$. An element $t\in G(k)$ is called strongly real if $t=\tau_1\tau_2$ where $\tau_i\in G(k)$ and $\tau_i^2=1$. We discuss when a semisimple real element is strongly real in $G(k)$. We investigate this question for classical groups and the groups of type $G_2$ in detail.

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Title: Entropy Power inequalities and monotonicity in central limit theorems
Speaker: Prof. Mokshay Madiman University of Yale, USA
Date: 23 February 2007
Venue: Lecture Hall I, Department of Mathematics, IISc

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Title: The spherical mean value operator for functions supported in a ball
Speaker: Prof. Rakesh (University of Delaware)
Date: 01 February 2007
Time: 4:00 pm
Venue: LH I

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