Lecture 2: Automorphy lifting theorems
Abstract: This lecture will talk about a technique used in the proof of Serre's modularity conjecture. This technique, called modularity/automorphy lifting, was developed by Wiles in his proof of Fermat's Last Theorem. It allows one to go "backwards" from a Galois representation to a modular form. (The "forward" direction from modular forms to Galois representations was known earlier by the work of Eichler, Shimura, Deligne and Serre.) Its likelyto be a key tool in any attack on higher dimensional analogs of Serre's conjecture.
11.30 Srinivasa Ramanujan Lecture