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.