SPEAKER:     Akshay Venkatesh

TITLE:    Weyl's law for cusp forms

ABSTRACT:

(all joint work with Elon Lindenstrauss) I'll describe a proof of Weyl's law for cusp forms on (congruence) locally symmetric spaces. (Even the existence of e.g. everywhere unramified cusp forms on G_2 was not known, as far as I know). The key new idea is a simple trace formula that uses only spherical test functions. I will explain this in the special case of the modular surface SL(2,Z)\H, where I'll outline elementary proofs of the existence of cusp forms and the Weyl law using this method.