Commutative Algebra seminar
Speaker: Sayed Sadiqul Islam (IIT Bombay)
Title: Frobenius endomorphism and applications
Time, day and date: 4:00:00 PM, Tuesday, February 4
Venue: Ramanujan Hall

Abstract
We explore the use of the Frobenius homomorphism to study the structure of local cohomology modules over rings of characteristic p. While local cohomology modules are not always finitely generated, we show that they exhibit important finiteness properties under certain conditions. Specifically, we use filter regular sequences to provide a proof that the set of associated prime ideals of the local cohomology modules is finite when the ring R has finite F-representation type or a finite singular locus. We also prove same results for regular rings of characteristic p.

Colloquium

Speaker : Aram Bingham

Day/Date/Time: 4:00 pm, Wednesday, 5th February

Venue : Ramanujan Hall

Title: Kronecker coefficients, polytopes, and complexity

Abstract : The “Kronecker coefficients problem” is one of the last major open  questions in the classical representation theory of symmetric groups. It  asks for a combinatorial rule describing the decomposition of tensor products of irreducible symmetric group representations, and a solution is known only in limited special cases. Kronecker coefficients have also
been the subject of much recent research motivated by the geometric complexity theory (GCT) program of Mulmuley and Sohoni, who hypothesized efficient computation of these numbers as part of a strategy to separate the computational complexity classes P and NP. We will discuss some of the main representation theoretic questions related to GCT and report some progress on computing Kronecker coefficients via discrete volumes of polytopes (joint work with Ernesto Vallejo).