Spectral theory of automorphic forms: infinite co-volume

Abstract: Given a Lie group $G$ and a discrete subgroup $\Gamma < G$, a critical tool used to analyze automorphic forms is to use spectral decomposition (e.g Selberg trace formula). For rank one hyperbolic manifolds the spectrum is either well understood or far beyond reach (e.g Selberg eigenvalue conjecture). In infinite volume the spectrum becomes linked to interesting geometric features of the manifold. In this talk I will survey some results about the spectrum of infinite co-volume subgroups and the connection to geometry and representation theory. This will include work with Dubi Kelmer and Alex Kontorovich, as well as work with Tobias Weich and Lasse Wolf.

number theory

Audience: researchers in the topic

International seminar on automorphic forms

Series comments: The password is the first Fourier coefficient of the modular j-function (as digits).