CMI Silver Jubilee Lecture

A. Raghuram, IISER, Pune

From Calculus to Number Theory (via Cohomology)

Monday, March 23, 2015

Abstract:

In our study of integral calculus, we come across various convergent series. Some of them are very well-known, having been made famous by the works of Euler, Leibniz, MacLaurin and Madhava (from the 14th century Kerala School of Mathematics). Such series happen to be prototypes of a subject within modern number theory called Special Values of L-functions. An L-function is a function of a complex variable that is attached to some interesting arithmetic or geometric data. The special values of these functions give structural information about such data. In this talk, I will weave a storyline starting with ancient formulas in Calculus leading up to some theorems and conjectures in modern Number Theory.