Résume | The analytic side of the theory of automorphic forms is
concerned with harmonic analysis on a locally symmetric space of
finite volume defined by a lattice $\Gamma$ in a semisimple Lie group
$G$. One of the main problems is the study of the spectrum of the
algebra of invariant differential operators on the corresponding
locally symmetric space or, more generally, with the study of the
spectral resolution of the right regular representation of $G$ in
$L^2(\Gamma\backslash G)$. One of the basic tools is the
Arthur-Selberg trace formula. In this talk I will discuss some recent
results concerning the asymptotic distribution of automorphic spectra
and I will also discuss some problems related to it. |