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Thu, 13 Dec 2018 10:16:40 +0530Thu, 13 Dec 2018 10:16:40 +0530Jekyll v3.7.3Lectures by H. Upmeier, Infosys Visiting Professor, from Friday, December 7, 2018<p>Professor H. Upmeier of the Marburg University would be visiting
Department of Mathematics, IISc, as the InfoSys Visiting Professor during the period Dec 4 - Feb 28.</p>
<p>During his stay, he intends to give a series of lectures on the broad theme of <em>“Geometric
Quantization in Complex and Harmonic Analysis”</em>. The first set of lectures will take place
according to the following schedule. The first lecture will be at 3:00 pm in LH-1, Department of Mathematics. All subsequent lectures will be at 4:00 pm in LH-1.</p>
<ul>
<li>Lecture 1: Friday, Dec 7</li>
<li>Lecture 2: Monday, Dec 10</li>
<li>Lecture 3: Wednesday, Dec 12</li>
<li>Lecture 4: Friday, Dec 14</li>
<li>Lecture 5: Monday, Dec 17</li>
<li>Lecture 6: Wednesday, Dec 19</li>
</ul>
<p>In this first set of lectures, he will discuss some basic material (connexions, curvature etc) and then cover,
with full proofs, the Borel-Weil-Bott theorem and the Kodaira embedding theorem. A second set of lectures
will be announced subsequently.</p>
Fri, 07 Dec 2018 00:00:00 +0530
http://math.iisc.ac.in/2018/12/07/upmeier.html
http://math.iisc.ac.in/2018/12/07/upmeier.html$\nu$-X symposium<p>We cordially invite you to the $\nu$-X symposium: an in-House faculty symposium
of the Department of Mathematics, IISc, on Tuesday, 27th November, 2018. This symposium is to mark the inauguration
of the new floor of the X-wing of the department.</p>
<p>The programme schedule for the symposium is as follows:</p>
<p><strong>Date:</strong> 27th November, 2018 (Tuesday)</p>
<p><strong>Venue:</strong> Lecture Hall-1, Department of Mathematics</p>
<table>
<thead>
<tr>
<th>Time</th>
<th>Title</th>
</tr>
</thead>
<tbody>
<tr>
<td>10.45 am - 11.00 am</td>
<td>Tea/coffee and opening remarks</td>
</tr>
<tr>
<td>11.00 am - 11.30 am</td>
<td>Subhojoy Gupta <em>Schwarzian equation on Riemann surfaces</em></td>
</tr>
<tr>
<td>11.30 am - 12.00 noon </td>
<td>Kaushal Verma <em>Polynomials that have the same Julia set</em></td>
</tr>
<tr>
<td>12.00 noon - 12.30 pm</td>
<td>Ved Datar <em>Stability and canonical metrics</em></td>
</tr>
<tr>
<td>12.30 pm - 2.00 pm</td>
<td>Break</td>
</tr>
<tr>
<td>2.00 pm - 2.30 pm</td>
<td>Manjunath Krishnapur <em>Comparing the largest eigenvalues of two random matrices</em></td>
</tr>
<tr>
<td>2.30 pm - 3.00 pm</td>
<td>Vamsi Pritham Pingali <em>Interpolation of entire functions</em></td>
</tr>
<tr>
<td>3.00PM - 3.15 pm</td>
<td>Tea/Coffee</td>
</tr>
<tr>
<td>3.15 pm - 3.45 pm</td>
<td>Apoorva Khare <em>Entrywise functions and 2x2 matrices: from Schur (and his student), to Loewner (and his student), to Schur</em></td>
</tr>
<tr>
<td>3.45 pm - 4:15 pm</td>
<td>Gautam Bharali <em>Hilbert and Minkowski meet Kobayashi and Royden, and</em> …</td>
</tr>
<tr>
<td>4.15 pm - 5.00 pm</td>
<td>High tea</td>
</tr>
</tbody>
</table>
<hr />
<p>Each lecture will be of 25 minutes with 5 minutes break for Q&A and change of speaker.</p>
<h3 id="abstracts">Abstracts</h3>
<h4 id="lecture-1-">Lecture 1 </h4>
<p><strong>Speaker:</strong> Subhojoy Gupta</p>
<p><strong>Title:</strong> Schwarzian equation on Riemann surfaces</p>
<p><strong>Abstract:</strong> There is a Riemann-Hilbert type problem for a certain second-order linear differential
equation that is still unsolved in the case that the surface has punctures. I will describe this, and
talk of how that relates to complex projective structures on surfaces via the Schwarzian
derivative. No background will be assumed.</p>
<hr />
<h4 id="lecture-2">Lecture 2</h4>
<p><strong>Speaker:</strong> Kaushal Verma</p>
<p><strong>Title:</strong> Polynomials that have the same Julia set</p>
<p><strong>Abstract:</strong> The purpose of this elementary talk will be to introduce some things that are known
about the following question: is there a relation between a pair of polynomials that have the
same Julia set?</p>
<hr />
<h4 id="lecture-3-">Lecture 3 </h4>
<p><strong>Speaker:</strong> Ved Datar</p>
<p><strong>Title:</strong> Stability and canonical metrics</p>
<p><strong>Abstract:</strong> A general principle in complex geometry is that existence of metrics with good
curvature properties must be related to some form of algebra-geometric stability. I will illustrate
this by using the example of conical Einstein metrics on a two dimensional sphere with marked
points. If time permits, I will touch upon the problem of constructing constant scalar curvature
metrics on kahler manifolds.</p>
<hr />
<h4 id="lecture-4">Lecture 4</h4>
<p><strong>Speaker:</strong> Manjunath Krishnapur</p>
<p><strong>Title:</strong> Comparing the largest eigenvalues of two random matrices</p>
<p><strong>Abstract:</strong> Let $T(m,n)$ denote the largest singular value of the complex Wishart matrix $W_{m,n}$
whose entries are independent random variables with real and imaginary parts that are
independent standard Gaussians. Riddhipratim Basu asked the question whether $T(n,n)$ is larger
than $T(n-1,n+1)$ in a stochastic sense, i.e., $P\{T(n,n)>x\} \ge P\{T(n-1,n+1)>x\}$ for all $x$. We provide a
positive answer by invoking a general coupling theorem of Lyons for determinantal point
processes. There are natural extensions of the question for which we do not know the answer.
For example, if the entries of W are real-valued Gaussian random variables.</p>
<hr />
<h4 id="lecture-5-">Lecture 5 </h4>
<p><strong>Speaker:</strong> Vamsi Pritham Pingali</p>
<p><strong>Title:</strong> Interpolation of entire functions</p>
<p><strong>Abstract:</strong> For various reasons (applied mathematics as well as algebraic geometry) it is
interesting to ask the following question :
Given a holomorphic function with “finite energy” on a subset of $\mathbb{C}^n$, can you extend it to all
of $\mathbb{C}^n$ still having finite energy ?
The answer to this question is known (almost completely) for a sequence of points in $\mathbb{C}$ with an
$L^2$ notion of the energy. After recalling the results in $\mathbb{C}$, we shall describe what happens in
higher dimensions with the help of an example or two.</p>
<hr />
<h4 id="lecture-6">Lecture 6</h4>
<p><strong>Speaker:</strong> Apoorva Khare</p>
<p><strong>Title:</strong> Entrywise functions and 2x2 matrices: from Schur (and his student), to Loewner (and his
student), to Schur</p>
<p><strong>Abstract:</strong> Given a smooth function $f : [0,1) \to \mathbb{R}$, and scalars $u_j$, $v_j$ in $(0,1)$, I will compute the
Taylor (Maclaurin) series of the function $F(t) := \det A(t)$, where $A(t)$ is the 2x2 matrix</p>
<script type="math/tex; mode=display">% <![CDATA[
\begin{pmatrix}
f( t u_1 v_1 ) & f( t u_1 v_2 ) \\
f( t u_2 v_1 ) & f( t u_2 v_2 )
\end{pmatrix}. %]]></script>
<p>C. Loewner computed the first two of these Maclaurin coefficients, in the thesis of his student
R.A. Horn (<em>Trans. AMS</em> 1969). This was in connection with entrywise functions preserving
positivity on matrices of a fixed dimension – the case of all dimensions following from earlier
work of Schur (<em>Crelle</em> 1911) and his student Schoenberg (<em>Duke</em> 1942).</p>
<p>It turns out that an “algebraic” family of symmetric functions is hiding inside this “analysis”. We
will see how this family emerges when one computes the second-order (and each subsequent
higher-order) Maclaurin coefficient above. This family of functions was introduced by Cauchy
(1800s), studied by Schur in his thesis (1901), and has featured extensively in recent
Eigenfunction Seminars (2017, 2018). As an application, I will generalize a determinant formula
named after Cauchy, which is the special case $f(x) = 1/(1-x)$ and $t=1$ above.</p>
<hr />
<h4 id="lecture-7">Lecture 7</h4>
<p><strong>Speaker:</strong> Gautam Bharali</p>
<p><strong>Title:</strong> Hilbert and Minkowski meet Kobayashi and Royden, and…</p>
<p><strong>Abstract:</strong> The Wolff–Denjoy theorem is a classical result that says: given a holomorphic
self-map f of the open unit disc, exactly one of the following holds true: either f has a fixedpoint in the open unit disc or there exists a point p on the unit circle such that ALL orbits under
the successive iterates of f approach p. This result is hard to generalise to higher dimensions,
although Abate has a precise analogue for strongly convex domains. A (real) convex domain
has an intrinsic distance associated to it – the Hilbert distance. Beardon simplified the proof of
Wolff and Denjoy and, in the process, showed that their conclusion in fact holds true for any
self-map of a convex domain that is contractive with respect to the Hilbert distance. This
strongly suggests that the Wolff–Denjoy theorem is only incidentally about holomorphic
functions. The latter observation is one of the motivations behind separate works with Zimmer
and Maitra. In these works, we show that the Wolff–Denjoy phenomenon extends to most
families of domains whose metric geometry we have some understanding of. We shall have no
time for proofs – we shall discuss motivations, analogies and intuitions.</p>
Tue, 27 Nov 2018 00:00:00 +0530
http://math.iisc.ac.in/2018/11/27/nu-x-symposium.html
http://math.iisc.ac.in/2018/11/27/nu-x-symposium.htmlSimon Marais List<p>Here is the list of students selected for participating in the
Simon Marais competition 2018.</p>
<p><strong>Singles category</strong></p>
<ol>
<li>Simran Jaykumar Gade</li>
<li>Anish Bhattacharya</li>
<li>Sarbartha Bhattacharya</li>
<li>Kartik Singh</li>
<li>Pranav Kasetty</li>
<li>Susheel Shankar</li>
<li>Archisman Panigrahi</li>
<li>Piyush Bhuwan Sati</li>
<li>Ayanesh Maiti</li>
<li>Samarth Hawaldar</li>
<li>Shafil Maheen N.</li>
<li>Chandrakant Harjpal</li>
<li>Chinmay S I</li>
<li>Rimika Jaiswal</li>
<li>Divij Mishra</li>
<li>Abhilash Mukherjee</li>
<li>Sagnik Barman</li>
<li>S. Yukthesh Venkat</li>
<li>M Prashant Krishnan</li>
<li>Nandagopal M.</li>
<li>Mihir Jain</li>
<li>M. Nikhesh Kumar</li>
<li>Kaushik Yashwant Bhagat</li>
<li>Achal Kumar</li>
<li>Praveen Jayakumar</li>
<li>Umang Bhat</li>
<li>Sagnik Barman</li>
<li>S. Shri Hari</li>
<li>Adit Vishnu P. M.</li>
<li>Bharat Vivan Thapa</li>
<li>S. R. Apuroopa</li>
</ol>
<p><strong>Pairs Category</strong></p>
<ol>
<li>Sutanay Bhattacharya, Pulkit Sinha</li>
<li>Ninad Hemant Huilgol, Chinmaya Kaushik</li>
<li>Yash Mehta, Vrunda Rathi</li>
<li>Nabarun Deka, Aaradhya Pandey</li>
<li>Ashim Kumar Dubey, S Sriram</li>
<li>R. Sainiranjan, Omkar Baraskar</li>
<li>Julian D’Costa, Gaurang S</li>
<li>Sidharth Soundararajan, Adithya Upadhya</li>
<li>Prakhar Gupta, Pranjal Pandurang Warade</li>
<li>Agneedh Basu, Arko Ghosh</li>
<li>Manan Bhatia, Pidaparthy Vasanth</li>
<li>Ishan Bhat, Kartikey Pratap Chauhan</li>
<li>Shreyas Raman, Sharan Srinivasan</li>
<li>Prathyush Prasanth Poduval, Aman Agarwal</li>
<li>Nishit Pandya, Shabarish Chenakkod</li>
<li>Anil Kumar, Shubham Kumar Pandey</li>
<li>Prathamesh Patil, Shibashish Mahapatra</li>
<li>Satabdee Sahoo, Sanjeet Panda</li>
<li>Adarsh Abraham Basumata, Abhinav Biswas</li>
<li>Aditi Ajith Pujar, Sukanya Majumder</li>
<li>Aarsh Chotalia, Mrugsen Gopnarayan</li>
<li>Pranshu Gaba, Aniruddh Balasubramaniam</li>
<li>Ankur Singh, Hitesh Kishore Das</li>
<li>Piush Ranjan Jena, Aman Anand</li>
</ol>
Wed, 03 Oct 2018 00:00:00 +0530
http://math.iisc.ac.in/2018/10/03/simon-marais-list.html
http://math.iisc.ac.in/2018/10/03/simon-marais-list.htmlIISc-NTU Mathematics Workshop<p>An IISc NTU workshop will be held on the occasion of the visit of the NTU, Singapore, delegation to IISc on September 19, 2018. The schedule of the lectures is as below.</p>
<ol>
<li>
<p><strong>Speaker:</strong> Arvind Ayyer, Department of Mathematics, IISc</p>
<p><strong>Time:</strong> 10.00 to 10.20 am</p>
<p><strong>Title:</strong> The combinatorics of odd and chiral partitions</p>
<p><strong>Abstract:</strong>
We say that a partition is odd if its dimension (computed by the hook-length formula) is odd. It turns out that the number a(n) of odd partitions of a positive integer is always a power of 2. This was proven independently by Macdonald and McKay. We will show that the subposet of the Young lattice consisting of odd partitions is a binary tree, and give an explicit recursive characterisation of this tree. </p>
<p>We say that a partition is chiral if the associated irreducible representation composed with the determinant map gives the sign character. Denote the number of chiral partitions of n by b(n). L. Solomon first considered the problem of enumeration of b(n) and Stanley posed it as an open problem in his book. We solve this problem by giving an explicit formula for b(n). We also show that the enumerations of a(n) and b(n) are closely related. The primary tool in our solution is J. Olsson’s theory of core towers.</p>
<p>This is joint work with A. Prasad and S. Spallone.</p>
</li>
<li>
<p><strong>Speaker:</strong> Frederique Oggier</p>
<p><strong>Time:</strong> 10.20 to 10.40 am</p>
<p><strong>Title:</strong> Facets of Algebraic Coding Theory</p>
<p><strong>Abstract:</strong> I will briefly explain what algebraic coding theory is about, and exhibit connections to different areas of algebra/number theory such as finite fields (as is classically the case), group theory (finite groups), lattice theory (and modular forms), and central simple algebras (over number fields).</p>
</li>
<li>
<p><strong>Speaker:</strong> Navin Kashyap, IISc</p>
<p><strong>Time:</strong> 10.40 to 11.00 am</p>
<p><strong>Title:</strong> Overview of research activities in coding theory at IISc</p>
<p><strong>Abstract:</strong>
We will give a brief and not-so-comprehensive overview of the research activities that are taking place at IISc, chiefly within the ECE Dept., in the broad area of coding theory.</p>
</li>
<li>
<p><strong>Speaker:</strong> Nicolas Privault</p>
<p><strong>Time:</strong> 11.00 to 11.20 am</p>
<p><strong>Title:</strong> Normal approximation for sums of discrete U-statistics, with application to Kolmogorov bounds in random subgraph counting.</p>
<p><strong>Abstract:</strong> We derive normal approximation bounds in the Kolmogorov distance for sums of discrete multiple integrals and U-statistics made of independent Bernoulli random variables. Such bounds are applied to normal approximation for renormalized subgraphs counts in the Erdős-Rényi random graph. This approach recovers recent results obtained for triangles and extends them to the general setting of arbitrary graphs, while improving other bounds derived in the Wasserstein distance.</p>
</li>
<li>
<p><strong>Speaker:</strong> Vijay Natarajan, Computer Science and Automation, IISc</p>
<p><strong>Time:</strong> 11.20 to 11.40 am</p>
<p><strong>Title:</strong> Topological Feature-Directed Visualization </p>
<p><strong>Abstract:</strong>
Scientific phenomena are often studied through collections of related scalar fields generated from different observations of the same phenomenon. Exploration of such data requires a robust distance measure to compare scalar fields for tasks such as identifying key events and establishing correspondence between features within a data set and across data sets. In this talk, I will first introduce the problem of symmetry detection in scientific data and its role in the design of feature-directed visualization methods. The goal is to identify regions of interest within the domain of a scalar field that remain invariant under transformations of both domain geometry and the scalar values. The problem generalises to similarity identification when applied to time-varying and multi-field data. I will present algorithms to detect symmetry and similarity and discuss applications to visualization, interactive exploration, and visual analysis of large and feature-rich scientific data. [http://vgl.csa.iisc.ac.in]</p>
</li>
<li>
<p><strong>Speaker:</strong> Xia Kelin</p>
<p><strong>Time:</strong> 11.40 am to 12.00 pm</p>
<p><strong>Title:</strong> Topological modeling and analysis of big data in biomolecules</p>
<p><strong>Abstract:</strong> The availability of gigantic structure and gene data in various databanks has brought a great opportunity for researchers to quantitatively understand the biomolecular structure, dynamics and functions. In this presentation, we discuss the application of topological data analysis (TDA) in biomolecular data analysis. We introduce molecular topological fingerprints (MTFs) for biomolecular structure characterization. MTFs are derived from the persistent homology analysis and provide a unique representation that balances the topological simplification and geometric details. Multidimensional persistent homology is proposed and further used to quantitatively predict the stability of protein folding configurations generated by steered molecular dynamics. An excellent consistence between my persistent homology prediction and molecular dynamics simulation is found. Further, multiresolution persistent homology is proposed to handle extremely large biomolecular data. The essential idea is to match the resolution with the scale of interest so as to represent large scale datasets with appropriate resolution. By appropriately tuning the resolution of a density function, we are able to focus the topological lens on the scale of interest. The proposed multiresolution topological method has potential applications in arbitrary data sets, such as social networks, biological networks and graphs. Moreover, we offer persistent homology based new strategies for topological denoising and for resolving ill-posed inverse problems in Cryo-EM data. Finally, the recent progress in the topology based drug design has been briefly discussed.</p>
</li>
</ol>
Wed, 19 Sep 2018 00:00:00 +0530
http://math.iisc.ac.in/2018/09/19/iisc-ntu-workshop.html
http://math.iisc.ac.in/2018/09/19/iisc-ntu-workshop.htmlNCM IST - PDE - Theory and Computation (2018).<p><a href="https://www.atmschools.org/2018/ist/pdetc/application-form">https://www.atmschools.org/2018/ist/pdetc/application-form</a></p>
Mon, 23 Jul 2018 00:00:00 +0530
http://math.iisc.ac.in/2018/07/23/IST-PDE.html
http://math.iisc.ac.in/2018/07/23/IST-PDE.htmlAdvanced Instructional School (AIS) on several complex variables for the period June 11 to June 23, 2018<p><a href="https://www.atmschools.org/2018/ais/scv/speakers-and-syllabus">Visit this page <br />
https://www.atmschools.org/2018/ais/scv/speakers-and-syllabus</a></p>
Mon, 11 Jun 2018 00:00:00 +0530
http://math.iisc.ac.in/2018/06/11/AIS.html
http://math.iisc.ac.in/2018/06/11/AIS.htmlIntegrated Ph.D Program 2018.<p><a href="http://math.iisc.ac.in/intphd2018result.html">CLICK HERE for list of candidates recommended for the Integrated PhD programme 2018.</a></p>
Fri, 01 Jun 2018 00:00:00 +0530
http://math.iisc.ac.in/2018/06/01/intphdresult.html
http://math.iisc.ac.in/2018/06/01/intphdresult.htmlPh.D Research Program 2018.<p><a href="http://math.iisc.ac.in/phd2018result.html">CLICK HERE for list of candidates recommended for the PhD programme 2018.</a></p>
Thu, 31 May 2018 00:00:00 +0530
http://math.iisc.ac.in/2018/05/31/phdresult.html
http://math.iisc.ac.in/2018/05/31/phdresult.htmlThe third Indo-Russian meeting in probability and statistics<p><a href="http://math.iisc.ernet.in/~manju/IndoRussian/indorussian.html">http://math.iisc.ernet.in/~manju/IndoRussian/indorussian.html</a></p>
Mon, 08 Jan 2018 00:00:00 +0530
http://math.iisc.ac.in/2018/01/08/probability-and-statistics.html
http://math.iisc.ac.in/2018/01/08/probability-and-statistics.htmlDiscussion meeting in Harmonic Analysis (in honour of Professor S Thangavelu)<p>A <a href="https://www.atmschools.org/2017/atmw/ha">wokshop in harmonic analysis</a> will be held at the department of mathematics from 11th of Dec to 16th of Dec. The workshop will be followed by a <a href="http://math.iisc.ac.in/~naru/dmha/">conference</a> (15th discussion meeting in harmonic analysis) which is in honour of S. Thangavelu who has turned sixty this year.</p>
Sun, 10 Dec 2017 00:00:00 +0530
http://math.iisc.ac.in/2017/12/10/harmonic-analysis.html
http://math.iisc.ac.in/2017/12/10/harmonic-analysis.html