Lecture 1: Modular forms and Galois representations
Abstract: This will be a broad overview of the connection between Galois groups and modular forms, and reciprocity laws in this context which link the two. One such law is Serre's modularity conjecture which has the particular consequence that there is a unique, irreducible, odd motive of rank 2 over the rationals, of weight 12 and with good reduction everywhere. It arises from the Ramanujan Delta-function.
11.30 Srinivasa Ramanujan Lecture