On the Bourgain-Dyatlov fractal uncertainty principle

  • Date:
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Wilhelm Schlag, Yale University
  • Contact person: Wolfgang Staubach
  • Seminarium

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.