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.