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Posted November 2, 2026
Last modified November 8, 2026

Applied Analysis Seminar Questions or comments?

Zhongkai Tao, IHES
Escape of mass for finite-area hyperbolic surfaces

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.