Number Theory Seminar

Speaker: Peter Zenz (McGill University)

Title: Arithmetic Quantum Chaos and Shifted Convolution Problems

Abstract: Arithmetic quantum chaos is a topic at the intersection of physics and number theory that is concerned about the distribution of mass of certain eigenfunctions on arithmetic surfaces. In this talk we explore questions around the distribution of mass of holomorphic Hecke cusp forms. More precisely, we show how to evaluate the quantum variance of holomorphic Hecke cusp forms on the vertical geodesic for smooth, compactly supported test functions. The variance is related to an averaged shifted-convolution problem that we evaluate asymptotically. During the talk we also compare the quantum variance computation for the vertical geodesic with the corresponding computation by Luo and Sarnak for the full fundamental domain and we highlight important differences.

The talk will be exclusively on Zoom. To receive the Zoom link, please contact one of the organizers if you are not on the mailing list of the Number Theory Seminar.