1. Outline & Descriptions

Using Galois representations associated to modular forms and modulo p modular forms theory, Serre and Swinnerton-Dyer proved (around 1970)

that the six primes of congruences found by Ramanujan for his Delta function are the only possible congruence primes. I want to explain their proof.

This is an instance of the interrelation between Galois representations and congruences which developed greatly after their work (Ribet, Wiles, Hida, Mazur-Wiles, etc…).

*This course/ lecture series will be on-site without recording or broadcasting.