From Langlands to Large Laplace Eigenfunctions

2:00 pm, Wednesday, 29th May

Abstract

It is a folklore conjecture that the sup norm of a Laplace eigenfunction on a compact hyperbolic surface grows more slowly than any positive power of the eigenvalue. In dimensions three and higher, this was shown to be false by Iwaniec-Sarnak and Donnelly, using methods from the theory of automorphic forms. I will present joint work with Farrell Brumley that strengthens these results and extends them to locally symmetric spaces associated to SO(p,q). Almost all of this talk will be accessible to analysts as well as number theorists.