Commutative Algebra seminar
Speaker: Sai Krishna P M S (IIT Bombay)
Host: Tony Puthenpurakal
Title: Number of generators of a Cohen-Macaulay ideal
Time, day and date: 4:00:00 PM, Tuesday, February 18
Venue: Ramanujan Hall

Abstract

Commutative Algebra seminar
We look at some results related to the bound on the number of generators of an ideal of a Noetherian local ring. Under the assumption that the ideal is Cohen-Macaulay, we get a bound on the number of generators of an ideal in a Noetherian local ring (R) in terms of the embedding dimension of the ring, the dimension, and the multiplicity of the quotient ring. We extend this result to any Cohen-Macaulay ideal of a Noetherian ring.

Title : Harmonic functions on groups

Date and Time: 18 February, 2025.  4 PM - 5 PM

Venue: Classroom 216, department of Mathematics

Abstract : In this talk, we will discuss about finitely generated groups
with a probability measure and the associated theory of harmonic
functions. We shall study the notions of (weak) Liouville property and
strong Liouville property, and see a characterisation of strong Liouville
property. Further, we shall discuss about Green speed, Green metric and
observe their relations with strong Liouville property. Finally, we study
slowly growing harmonic functions and how they descend onto finite index
subgroups. This is based on an ongoing joint work with Mayukh Mukherjee
and Soumyadip Thandar.