EVENT DETAILS AND ABSTRACT

Title: Kleinian Schottky groups, Patterson-Sullivan measures, and Fourier decay
Speaker: Wenyu Pan
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

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 set of Kleinian Schottky groups and show the Fourier transform of the associated Patterson-Sullivan measures enjoy polynomial decay. This generalizes a result of Bourgain-Dyatlov for convex cocompact Fuchsian groups. The proof includes an estimate on the decay of exponential sums based on Bourgain-Gamburd sum-product estimate on $\mathbb{C}$ and a regularity estimate for stationary measures for certain random walks on linear groups. This is a joint work with Jialun Li and Frédéric Naud.