


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 
Abstract 
I gave a series of about 50 lectures on Algebraic Stacks and Moduli spaces in the Department of Mathematics, IITB, 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 LieKolchin theorem. 
Commutative Algebra Seminar 

Date 
Tuesday, 2 April, 2024, 45 pm 
Venue 
Room 215 
Host 
Tony J. Puthenpurakal 
speaker 
Om Prakash 
Affiliation 
IIT Bombay 
Title 
Numerical Semigroups and associated Semigroup RingsI 
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 CohenMacaulay type of the numerical semigroup ring $k[S]$ corresponds to the number of pseudoFrobenius elements of $S$. Consequently, we derive a wellknown result concerning Gorenstein numerical semigroup rings (credited to Kunz) asserting that k[S] is Gorenstein if and only if S is symmetric. 
Algebraic groups Seminar
Date
Thursday, 4 April, 4 pm
Venue
Room 105
Host
Dipendra Prasad
speaker
Deep Makadiya
Affiliation
IIT Bombay
Title
Regular elements of semisimple algebraic groups
Abstract
We will continue with the seminar on Algebraic groups reading the paper of Robert Steinberg, Regular elements of semisimple algebraic groups Publications mathématiques de l’I.H.É.S., tome 25 (1965), p. 4980

Topology and Related Topics Seminar 
Date 
Friday, 5 April 2024, 10.15 am 
Venue 
Ramanujan Hall 
Host 
Rekha Santhanam 
speaker 
Sudarshan Gurjar 
Affiliation 
IIT Bombay 
Title 
Vector bundles and Characteristic Classes 
Abstract 
This is the third talk in the series of three talks. We will give an introduction to the characteristic classes of a vector bundle. Characteristic classes are invariants of a vector bundle taking values in the singular cohomology of the base and satisfying the obvious functoriality property concerning pullback. They are the measure of the nontriviality of the vector bundle. 

Algebraic geometry seminar 
Date 
Friday, 5 April, 11.30 am 
Venue 
Ramanujan Hall 
Host 
Sudarshan Gurjar 
speaker 
Nitin Nitsure 
Affiliation 
Bhaskaracharya Pratishthana, Pune 
Title 
Introduction to the Tohoku (1957) paper of Grothendieckpart 1 
Abstract 
In 1957, Alexander Grothendieck published a long paper in 

Analysis seminar 
Date 
Friday, April 5, 4 pm  5 pm 
Venue 
Ramanujan Hall 
Host 
Chandan Biswas 
speaker 
Prachi Mahajan 
Affiliation 
IIT Bombay 
Title 
The Squeezing function & the Fridman invariant 
Abstract 
The squeezing function and its dual, the Fridman invariant, are biholomorphic invariants, both of which capture the coarse metric geometry of the given domain. I will describe some results on the squeezing function and Fridman invariant such as their boundary behavior, their utility in classifying the unit ball under various hypotheses, and estimates near the boundary of the given domain. In the second part, I will compare this pair of invariants by showing that they are both equally capable of determining the boundary geometry of a bounded domain if their boundary behavior is apriori known. 