Simon Marshall (Northwestern University)




Talk in the Analysis Seminar 
Tuesday, September 10, 2013, 4:00 p.m., B139 VV

L^p bounds for eigenfunctions on locally symmetric spaces

Abstract: There is a classical theorem of Sogge that provides bounds for the L^p norms of a Laplace eigenfunction on a compact
Riemannian manifold, which are sharp on the sphere and for spectral clusters. I will present a generalization of this theorem to
eigenfunctions of the full ring of invariant differential operators on a locally symmetric space, as well as a theorem on the
restriction of eigenfunctions to maximal flat subspaces. Time permitting, I will discuss ways in which these bounds can be improved
using inputs from number theory.


Talk in the Number Theory  Seminar 
Thursday, September 12, 2013
Endoscopy and cohomology growth on U(3)

Abstract: I will use the endoscopic classification of automorphic forms on U(3) to determine the asymptotic cohomology growth of
families of complex-hyperbolic 2-manifolds.