Abstract

Since Ribet’s groundbreaking work on the converse to Herbrand’s theorem, congruences between modular forms have played an important role in number theory. In this talk, I will begin by reviewing Ribet’s work through the perspective of Mazur’s hexagon. I will then discuss how this framework can be generalized to higher-dimensional settings. In particular, I will explain aspects of the work of Skinner–Urban and its connections with Iwasawa theory. If time permits, I will discuss some of my current work on congruences for $U(3)$.

Organizers

Flora Poon (NCTS), Rahul Rajkumar (AS)