Bay Area Microlocal Analysis Seminar: Long time propagation and fractal uncertainty principle

Seminar | October 10 | 4-5 p.m. | 383N Stanford

  Building 380, Stanford, CA 94305

 Semyon Dyatlov, UC Berkeley

 Department of Mathematics

I will show a frequency-independent lower bound on mass of eigenfunctions on surfaces of variable negative curvature. This was previously done in the case of constant curvature in joint work with Jin, relying on the fractal uncertainty principle proved in joint work with Bourgain. I will focus on the new components needed to handle the case of variable curvature, in particular propagation of quantum observables up to local Ehrenfest time. Joint work in progress with Long Jin and Stéphane Nonnenmacher.