Asymptotics of automorphic spectra and the trace formula

Abstract

This paper is a survey article on the limiting behavior of the discrete spectrum of the right regular representation in $L^2(\Gamma\bs G)$ for a lattice $\Gamma$ in a reductive group $G$ over a number field. We discuss various aspects of the Weyl law, the limit multiplicity problem, the analytic torsion, and applications to the cohomology of arithmetic groups.