Speaker
Zhongkai Tao, IHES
Abstract
On a finite-area hyperbolic surface with cusps, we prove that L^2 eigenfunctions cannot concentrate too much deep in the cusps as the eigenvalue goes to infinity. For arithmetic surfaces, a stronger estimate was known due to Soundararajan. Our result uses the nonlinear uncertainty principle developed by Cohen and Dyatlov. This is joint work with Alex Cohen and Zhenhao Li.