Restricted arithmetic quantum unique ergodicity

Peter Humphries, University of Virginia
IAS - Simonyi Hall Seminar Room SH-101

Meeting ID:  920 2195 5230

Passcode:    The three-digit integer that is the cube of the sum of its digits.

The quantum unique ergodicity conjecture of Rudnick and Sarnak concerns the mass equidistribution in the large eigenvalue limit of Laplacian eigenfunctions on negatively curved manifolds. This conjecture has been resolved by Lindenstrauss when this manifold is the modular surface assuming these eigenfunctions are additionally Hecke eigenfunctions, namely Hecke-Maass cusp forms. I will discuss a variant of this problem in this arithmetic setting concerning the mass equidistribution of Hecke-Maass cusp forms on submanifolds of the modular surface.