Bay Area Microlocal Analysis Seminar: Control and stabilization on hyperbolic surfaces

Seminar | March 13 | 2:10-3 p.m. | 732 Evans Hall

 Long Jin, Purdue University

 Department of Mathematics

In this talk, we discuss some recent results concerning the control and stabilization on a compact hyperbolic surface. In particular, we show that

the Laplace eigenfunctions have uniform lower bounds on any nonempty open set;

the linear Schrödinger equation is exactly controllable by any nonempty open set; and

the energy of solutions to the linear damped wave equation with regular initial data decay exponentially for any smooth damping function.

The new ingredient is the fractal uncertainty principle for porous sets by Bourgain–Dyatlov. This is partially based on joint work with Semyon Dyatlov.