The Algebra & Combinatorics Seminar meets on Fridays from 3–4
pm, in Lecture Hall LH1 of the IISc Mathematics Department – or
online in the Autumn 2020 semester. The organizers are R. Venkatesh and
Apoorva Khare.

Bharathwaj Palvannan
(National Center for Theoretical Sciences, Taiwan) 
Aug 28, 2020 
Codimension two
cycles in Iwasawa theory 
(3
pm, Fri) 

Abstract.
In classical Iwasawa theory, one studies a relationship called the
Iwasawa main conjecture, between an analytic object (the padic
Lfunction) and an algebraic object (the Selmer group). This relationship
involves codimension one cycles of an Iwasawa algebra. The topic of
higher codimension Iwasawa theory seeks to generalize this relationship.
We will describe a result in this topic using codimension two cycles,
involving an elliptic curve with supersingular reduction. This is joint
work with Antonio Lei.

Sandeep Varma (TIFR, Mumbai) 
Sep 4, 2020 
Some Bernstein
projectors for $SL_2$ 
(3
pm, Fri) 

Abstract.
Let $G$ be the group $SL_2$ over a finite extension $F$ of
$\mathbb{Q}_p$, $p$ odd. I will discuss certain distributions on $G(F)$,
belonging to what is called its Bernstein center (I will explain what
this and many other terms in this abstract mean), supported in a certain
explicit subset of $G(F)$ arising from the work of A. Moy and G. Prasad.
The assertion is that these distributions form a subring of the Bernstein
center, and that convolution with these distributions has very agreeable
properties with respect to orbital integrals. These are 'depth $r$
versions' of results proved for general reductive groups by J.F. Dat, R.
Bezrukavnikov, A. Braverman and D. Kazhdan.

Charanya Ravi (Universität Regensburg,
Germany) 
Sep 8, 2020 
Algebraic
Ktheory of varieties with group actions 
(unusual day: 3
pm, Tue) 

Abstract.
Cohomology theories are one of the most important algebraic invariants of
topological spaces and this has inspired the definition of several
different cohomology theories in algebraic geometry. In this talk, we
focus on algebraic Ktheory, which is one such classical cohomological
invariant of algebraic varieties. After motivating and introducing this
notion, we discuss several fundamental properties of algebraic Ktheory
of varieties with algebraic group actions. Wellknown examples of
varieties with group actions include toric varieties and flag varieties.

Apoorva Khare (IISc Mathematics) 
Sep 18, 2020 
Totally
positive matrices, Pólya frequency sequences, and Schur
polynomials
(Joint with the APRG Seminar) 
(3
pm, Fri) 

Abstract.
I will discuss totally positive/nonnegative matrices and kernels,
including Polya frequency (PF) functions and sequences. This includes
examples, history, and basic results on total positivity, variation
diminution, sign nonreversal, and generating functions of PF sequences
(with some proofs). I will end with applications of total positivity to
old and new phenomena involving Schur polynomials.

Ignazio Longhi (IISc
Mathematics) 
Sep 25, 2020 
Densities on
Dedekind domains, completions and Haar measure 
(3
pm, Fri) 

Abstract.
A traditional way of assessing the size of a subset X of the integers is
to use some version of density. An alternative approach, independently
rediscovered by many authors, is to look at the closure of X in the
profinite completion of the integers. This for example gives a quick,
intuitive solution to questions like: what is the probability that an
integer is squarefree? Moreover, in many cases, one finds that the
density of X can be recovered as the Haar measure of the closure of X. I
will discuss some things that one can learn from this approach in the
more general setting of rings of integers in global fields. This is joint
work with Luca Demangos.


Abstract.
TBA

Deniz Kus (RuhrUniversity Bochum, Germany) 
Oct 23, 2020 
TBA 
(3
pm, Fri) 

Abstract.
TBA


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Shifra Reif (BarIlan University, Israel)  Nov 13, 2020 
Denominator
identities for Lie superalgebras 
(3
pm, Fri) 

Abstract.
TBA

Sanoli Gun (IMSc, Chennai)  Nov 20, 2020 
TBA 
(3
pm, Fri) 

Abstract.
TBA


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TBA

2019–20
2018–19
