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Wilhelm Schlag: On the Bourgain-Dyatlov fractal uncertainty principle

Time: Thu 2019-03-14 15.30 - 16.30

Location: Seminar Hall Kuskvillan, Institut Mittag-Leffler

Lecturer: Wilhelm Schlag, Yale University

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.