In this talk, we present a uniform lower bound for the mass in any fixed nonempty open set of normalized Laplacian eigenfunctions on negatively curved surfaces, independent of eigenvalues. The result extends previous joint work with Semyon Dyatlov on surfaces with constant negative curvature. The proof relies on microlocal analysis, chaotic behavior of the geodesic flow and a new ingredient from harmonic analysis called Fractal Uncertainty Principle by Jean Bourgain and Semyon Dyatlov. Further applications include control for Schr\"{o}dinger equation and exponential decay of energy for damped waves. This is based on joint work with Semyon Dyatlov and St\'{e}phane Nonnenmacher.

会议密码：220318