



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. 