Title: Modular forms mod p
Speaker: Joël Bellaïche
Speaker Info: Brandeis
Brief Description:
Special Note:
Abstract:
Starting as a conceptual tool to explain Ramanujan's congruences involving the tau function, the theory of modular forms modulo a prime p experienced a rapid development in the 70's and 80's with the works of Atkin, Swinnerton-Dyer, Serre, Tate and many others. Then this development almost stopped for two decades, leaving some of the most fundamental questions unanswered. In the last four years, the theory has experienced a revival; many old questions have been solved and some new ones have arisen. In this talk I will present a panorama of the subject, insisting on the recent progresses, and discuss in detail some of them (structure of the Hecke algebras, asymptotics of the coefficients, etc.), as well as some perspectives of applications and generalizations to higher groups automorphic forms.Date: Monday, September 29, 2014