The fractal uncertainty principle

Analysis Seminar
Wednesday, November 28, 2018 - 1:55pm for 1 hour (actually 50 minutes)
Skiles 005
Rui Han – Georgia Tech
Shahaf Nitzan
Recently Bourgain and Dyatlov proved a fractal uncertainty principle (FUP), which roughly speaking says a function in $L^2(\mathbb{R})$ and its Fourier transform can not be simultaneously localized in $\delta$-dimensional fractal sets, $0<\delta<1$. In this talk, I will discuss a joint work with Schlag, where we obtained a higher dimensional version of the FUP. Our method combines the original approach by Bourgain and Dyatlov, in the more quantitative rendition by Jin and Zhang, with Cantan set techniques.