Dear all,


Today's speaker at the Analysis and Probability Seminar is Wenyu Pan 
from University of Chicago. The title of her talk is "Kleinian Schottky 
Groups, Patterson-Sullivan Measures, and Fourier Decay".

The talk will begin at 1:30pm (Eastern Time) on Zoom, doors open at 
1:25pm. The details are as follows:

Join Zoom Meeting
https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fzoom.us%2Fj%2F93189118174%3Fpwd%3DSW1USXVqOHpyaDFlZ3VRdHBPMmJNUT09&data=04%7C01%7C%7C91daf7f4bf5d41cb240108d88d5a6e25%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C637414766817933578%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=9OlUzjUO2meoUd1qG2YhjIa3hkXRGouew6v7fp0JG%2Fo%3D&reserved=0

Meeting ID: 931 8911 8174
Passcode: AP

Abstract: We show that the Fourier transform of the Patterson-Sullivan 
measure of a Kleinian Schottky subgroup of 
$\operatorname{PSL}_2(\mathbb{C})$ enjoys polynomial decay. This 
generalizes a result of Bourgain-Dyatalov for convex-cocompact Fuchsian 
groups and uses the decay of exponential sums based on Bourgain-Gamburd 
sum-product estimate on $\mathbb{C}$. These bounds on exponential sums 
require a delicate non-concentration hypothesis, which is proved using 
some representation theory and regularity estimates for stationary 
measures of certain random walks on linear groups. This is joint work 
with Jialun Li and Frédéric Naud.


Best,

Yunfeng