A showcase of Siegel modular forms | Department of Mathematics

A showcase of Siegel modular forms

Event Information
Event Location: 
GAB 461 (Refreshments at 3:30 in 472)
Event Date: 
Monday, March 28, 2016 - 4:00am

(Elliptic) modular forms are well-known because of their crucial role in Weil's proof of Fermat's last theorem. A bit less prominently, but equally
useful, they occur in many contemporary fields of mathematics and applications: Combinatorics, representation theory, algebraic geometry, enumerative
geometry, topological field theory, string theory, etc.

One possible generalization of elliptic modular forms that appeared in Weil's proof are Siegel modular forms. This direction of generalization is natural
from a geometric, a representation theoretic, and a classical analytic perspective. Despite the severe complications encountered in the theory of
Siegel modular forms, they have remained a popular and rewarding field of study. We give a brief tour of two recent developments in Siegel modular
forms: The "endoscopic" classification by James Arthur, and algebraization results in the spirit of formal geometry by the speaker.

This will be a survey talk. No prior knowledge of modular forms is required.