The spectrum of a locally symmetric space, such as SL_n(Z)

SL_n(R) / SO(n), is of fundamental importance in

number theory and automorphic forms. One type of questions which arise is

the asymptotic behavior of the spectrum

as we vary the lattice. This goes back to DeGeorge-Wallach. I will discuss

some of the history of this question and recent progress.

Joint work with Tobias Finis and Werner Muller.