The fractal uncertainty principle

Series: 
Analysis Seminar
Wednesday, November 28, 2018 - 1:55pm
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Georgia Tech
Organizer: 
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&nbsp;can not be simultaneously localized in $\delta$-dimensional&nbsp;fractal sets, $0<\delta<1$. In this talk, I will discuss a joint work with Schlag, where we obtained&nbsp;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.