Résumé
Fractal uncertainty principle states that if a function is Fourier localized to a fractal set, then only a very small part of its mass can live on another fractal set. In this talk I will state the fractal uncertainty principle and discuss two proofs: a simpler one in the case of arithmetic Cantor sets (joint work with Long Jin) and a more complicated one for general fractal subsets of the real line (joint work with Jean Bourgain).
