Speaker
Félix Lequen, Université Sorbonne Paris-Nord
Abstract
In this talk, we explain how to generalise the work of Jordan-Sahlsten on the Gauss map to prove Fourier decay for Patterson-Sullivan measures of Schottky subgroups of isometries of the hyperbolic plane which have exponent larger than 1/2. The proof is by approximation by Lebesgue measure and the stationary phase method, and avoids Bourgain’s sum-product theorem or renewal theory. This allows us to get a quantitative polynomial rate of decay. This is joint work with Tuomas Sahlsten.