


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. 