Speaker: Alexander Gorodnik
Date: January 20, 2026
Affiliation: University of Zurich

Abstract: We discuss the problem of Diophantine approximation on algebraic groups and relate this problem to the behavior of certain averaging operators acting on homogeneous spaces. It turns out that the problem of approximation is closely linked to understanding the spectral decomposition of automorphic representations. Currently, establishing the optimal approximation presents a significant challenge due to the presence of representations with slow decay rates. We discuss a method that overcomes this difficulty based on multiplicity estimates. The talk is based on joint work with M. Francyk, A. Ghosh, and A. Nevo.