Faculty Area Research (FARS)
Our first speaker for this quarter is Richard Taylor.
Title: The role of regularity in the Langlands program
Abstract: The Langlands program posits a remarkable relationship between objects in arithmetic algebraic geometry (Diophantine equations) and automorphic forms (functions on Lie groups invariant by a discrete subgroups). Great progress has been made in the last 50 years, almost all of it in the so called `regular case'. Curiously, from the point of view of automorphic forms the regularity restriction may not seem so serious, but from the point of view of an algebraic geometer it is, in Serre's words, `terrible'. My aim in this talk is to try to explain the distinction between the regular and irregular cases, and draw attention to what I consider the most fundamental problem facing those working in this area.