Algebraic geometry seminar

Date

Tuesday, 2 April, 11.30 am

Venue

Room 215

Host

Sudarshan Gurjar

speaker

Nitin Nitsure

Affiliation

Bhaskaracharya Pratishthana, Pune

Title

Overview and summary of my 50 lectures on Algebraic Stacks and
Moduli spaces, 2022-24.

Abstract

I gave a series of about 50 lectures on Algebraic Stacks and Moduli spaces in the Department of Mathematics, IIT-B,  spread across four semesters from 2022 to 2024. This is the final lecture of this series, in which I will summarise the main themes, and make suggestions for further study.

Algebraic groups Seminar

Date

Tuesday, April 2, 2024, 4 pm

Venue

Ramanujan Hall

Host

Shripad M. Garge

speaker

Akash Yadav

Affiliation

IIT Bombay

Title

Connected solvable groups

Abstract

We begin studying connected, solvable, linear algebraic groups starting with the Lie-Kolchin theorem.

Commutative Algebra Seminar

Date

Tuesday, 2 April, 2024, 4-5 pm

Venue

Room 215

Host

Tony J. Puthenpurakal

speaker

Om Prakash

Affiliation

IIT Bombay

Title

Numerical Semigroups and associated Semigroup Rings-I

Abstract

In this series of two lectures, we will study numerical semigroups and their associated semigroup rings. Initially, we will define numerical semigroups, state their fundamental properties, and introduce relevant invariants. Subsequently, we aim to prove the following fundamental results: (i) The Frobenius number of a numerical semigroup S equals the degree, viewed as a rational function, of the Hilbert series of the numerical semigroup ring k[S]. (ii) The Cohen-Macaulay type of the numerical semigroup ring $k[S]$ corresponds to the number of pseudo-Frobenius elements of $S$.  Consequently, we derive a well-known result concerning Gorenstein numerical semigroup rings (credited to Kunz) asserting that k[S] is Gorenstein if and only if S is symmetric.