On the Geometry and Arithmetic of Non-Spherical Maass Forms

This lecture, part of the Joint Princeton University/Institute for Advanced Study Number Theory series, features Djordje Milicevic discussing the geometry and arithmetic of non-spherical Maass forms. Explore central predictions of arithmetic quantum chaos including the Quantum Unique Ergodicity conjecture and the sup-norm problem, focusing on how they relate to mass distribution of automorphic forms. Discover recent results, developed jointly with Blomer, Harcos, and Maga, that solve the sup-norm problem for non-spherical Maass forms with increasing K-type dimensions in two settings: arithmetic quotients of SL(2,C) and SL(3,R). Learn about the detailed mass concentration of spherical trace functions of arbitrary K-type and the resulting new counting problems of Hecke correspondences near special submanifolds. The talk takes place on May 1, 2025, at 3:30pm in Simonyi 101 with remote access available.