EVENT DETAILS AND ABSTRACT

Title: Fractal Uncertainty Principles and Applications to Some Problems in Quantum Chao
Speaker: Long Jin
Speaker Info: Purdue
Brief Description:
Special Note:
Abstract:

In this talk, we discuss a new tool called fractal uncertainty principle and its applications in quantum chaos. Roughly speaking, a fractal uncertainty principle states that a function cannot be localized close to fractal sets in both position and frequency. It was first developed by Dyatlov-Zahl and Bourgain-Dyatlov for studying essential spectral gaps for convex co-compact hyperbolic manifolds. In a joint work with Semyon Dyatlov, we also use the fractal uncertainty principle of Bourgain-Dyatlov to prove that semiclassical measures for Laplacian eigenfunctions on compact hyperbolic surfaces must have full support on the cosphere bundle. For this talk, we shall discuss various results in this new direction and in particular, a simple model called open quantum maps to illustrate some basic ideas behind the fractal uncertainty principle.