Arithmetic applications of the trace formula and asymptotic orthogonality of tempered representations

Abstract: In the first part of the talk, I will discuss an approach based on the trace formula to investigate the conjecture of K. Buzzard and T. Gee that every C-algebraic automorphic representation of a connected reductive algebraic group defined over a number field is C-arithmetic. In the second part, I will present a joint work with Anne-Marie Aubert dedicated to the proof of the Archimedean case of the asymptotic form of Schur's orthogonality for K-finite matrix coefficients of tempered representations of semisimple groups proposed by D. Kazhdan and A. Yom Din.

algebraic geometrynumber theory

Audience: researchers in the topic

Luxembourg Number Theory Day 2024