Modularity of Galois Representations

MEMBERS SEMINAR
Topic:Modularity of Galois Representations
Speaker:Chandrashekhar Khare
Affiliation:University of California, Los Angeles
Date:Monday, November 22
Time/Room:2:00pm - 3:00pm/S-101

In this expository talk, I will outline a plausible story of how the study of congruences between modular forms of Serre and Swinnerton-Dyer, which was inspired by Ramanujan's celebrated congruences for his tau-function, led to the formulation of Serre's modularity conjecture. I will give some hints of the ideas used in its proof given in joint work with J-P. Wintenberger. I will end by pointing out just one of the many interesting obstructions to generalising the strategy of the proof to get modularity results in more general situations.