3:30 pm, Seminar Hall
Raising The Level For Automorphic Forms
Congruences satisfied by modular forms has been a central theme of study in Number Theory. In particular, the problem of finding an eigenform congruent to a given eigenform (of different levels) is of great interest. Ken Ribet proved fundamental results of this sort in the 80s and 90s. In this talk, we explain his one such result, which is concerned with finding eigenforms that are congruent to a given eigenform and are of a higher level than the given one, hence the name "level-raising". Time permitting, we will sketch how one might extend this setup to automorphic forms on groups of higher rank, and state recent results by Jack Thorne in this regard.