Koç University, Mathematics Seminar

Date & Time: Tuesday, January 05, 14:00-15:00

Place: SCI 129

Speaker: Ali Altuğ (Columbia University)

Title: Arthur-Selberg Trace Formula and Related Problems

Abstract: The Arthur-Selberg trace formula is a vast generalization of the classical Poisson summation formula to the non-abelian setting of a reductive algebraic group. It is one of the most powerful and prominent tools in number theory and the modern theory of automorphic forms. In his recent proposal, called “Beyond Endoscopy”, Langlands proposed a strategy to attack the general functoriality conjectures using the trace formula in a non-standard manner. In this talk I will first introduce the strategy of beyond endoscopy, then talk about the trace formula and the problems one encounters in trying the execute it in the context of the group GL(2). I will then report on recent progress towards these problems. If time permits I will also talk about recent questions about the trace formula itself, raised by Arthur, that are motivated by considerations related to beyond endoscopy, and certain more arithmetic results that can be obtained via methods that go into beyond endoscopy.

Speaker's Brief Biography: He is a Ritt Assistant Professor at Columbia University interested in analytic number theory and the theory of automorphic forms. Before arriving at Columbia, he was a PhD student at Princeton University working with Robert Langlands and Peter Sarnak. His research is mainly focused around analytic aspects of automorphic forms, L-functions, functoriality conjectures, and trace formulas.