Algebra and Number theory Seminar

Ian Petrow ETH
Title: The Weyl law for algebraic tori
Abstract: Families are powerful tools across all of mathematics. This talk will be about families of automorphic representations and their applications in number theory. There is no canonical definition of a family of automorphic forms/representations, but several ad-hoc definitions have been proposed. Here, a basic but still difficult question is: given a reductive algebraic group G, how many irreducible automorphic representations of bounded conductor are there? I will present a complete answer to this question in the case that G is a torus defined over a number field.