On the Bourgain-Dyatlov fractal uncertainty principle
- Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
- Lecturer: Wilhelm Schlag, Yale University
- Contact person: Wolfgang Staubach
Abstract: I will discuss uncertainty principles, including the Bourgain-Dyatlov breakthrough result from late 2016. Using harmonic analysis of the type which arises in the Beurling-Malliavin theorem, they showed (in a quantitative way) that a function on the line cannot be supported on fractal sets both in the physical and Fourier variables. The higher-dimensional version of this theorem remains open. I will describe some partial progress by Rui Han and myself. The main obstacle here is the absence of a higher-dimensional version of the Beurling-Malliavin theorem.