Mon, October 21, 2024
4:00 pm - 5:00 pm
Math Tower (MW) 154
Simon Marshall
University of Wisconsin-Madison
Title
Large values of eigenfunctions on hyperbolic manifolds
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. I will present joint work with Farrell Brumley that strengthens these results, and extends them to locally symmetric spaces associated to SO(n, m). The proof relies on a distinction principle for automorphic periods, involving the theta lift to Sp_{2m}.