|Topic:||Modularity of Galois Representations|
|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.