**Date & Time:** November 22, 2010; 16:30-17:30.

**Venue:** Ramanujan Hall

**Speaker:** Dr Rajan Sundaravaradhan

**Abstract:** Lectures on Tate’s thesis

In the early 20th century, Hecke defined L-functions over number fields which were generalizations of Dirichlet L-functions and he also showed that these Hecke L-functions satisfy a functional equation. John Tate in his seminal thesis gave an elegant treatment of the func- tional equations of the Hecke L-functions, by using Fourier analytic techniques on Adeles and Ideles, which provided a great advance over the classical techniques used by Hecke. In these lectures we will give an overview of the main ideas in this thesis.