Seminar at SMU Delhi

October 24, 2011 (Monday) , 3:30 PM at Webinar (Note: unusual day)
Speaker: Jacques Tilouine, Université Paris 13
Title: Congruences between modular forms and eigenvarieties
Abstract of Talk
Congruences between modular forms have been discovered by Ramanujan around 1910; their systematic study started only in 1970 with the work of Serre and Swinnerton-Dyer. A new phenomenon, congruences between cusp forms, has been discovered numerically by the japanese mathematician Doi in 1975. These congruences have been systematized by Hida and Coleman in the 80's in what is called $p$-adic families of cusp forms; they are now best seen through the geometry of a curve (or even a higher dimensional variety) called the Eigenvariety (or the Hecke Variety). I'll summarize these progresses with examples.