Kleinian Schottky groups, Patterson-Sullivan measures, and Fourier decay

Vortrag von Dr. Wenyu Pan

Sprecher eingeladen von: Prof. Dr. Corinna Ulcigrai

Datum: 17.10.19  Zeit: 15.30 - 16.30  Raum: Y13L11/13

We will start with the notion of Fourier dimension of a subset of $\mathbb{R}^d$. We will then focus on the particular case of the limit sets of Kleinian Schottky groups and show the the Fourier transform of the associated Patterson-Sullivan measures enjoy polynomial decay. This generalizes a result of Bourgain-Dyatlov for convex co-compact Fuchsian groups. The proof includes an estimate on the decay of exponential sums and a regularity estimate for stationary measures of certain random walks on linear groups. This is a joint work with Jialun Li and Fréderic Naud.