Analysis, Spectra and Number Theory, a Conference in Honor of Peter Sarnak’s 61st Birthday

In this talk I will discuss the asymptotic behaviour of the discrete (resp. cuspidal) spectrum of arithmetic groups with respect to the growth of various parameters such as the level of congruence subgroups, the analytic conductor and the rank of local systems. I will also discuss the relation with the growth of torsion in the cohomology of arithmetic groups. The main tool is a refinement of the Arthur trace formula.