# Elliptic measures and the geometry of domains

 Analysis Seminar Topic: Elliptic measures and the geometry of domains Speaker: Zihui Zhao Affiliation: Member, School of Mathematics Date: Thursday, February 14 Time/Room: 1:00pm - 2:00pm/Simonyi Hall 101 Video Link: https://video.ias.edu/analysis/2019/0214-ZihuiZhao

Given a bounded domain $\Omega$, the harmonic measure $\omega$ is a probability measure on $\partial \Omega$ and it characterizes where a Brownian traveller moving in $\Omega$ is likely to exit the domain from. The elliptic measure is a non-homogenous variant of harmonic measure. Since 1917, there has been much study about the relationship between the harmonic/elliptic measure $\omega$ and the surface measure $\sigma$ of the boundary. In particular, are $\omega$ and $\sigma$ absolutely continuous with each other? In this talk, I will show how a positive answer to this question implies that the corresponding domain enjoys good geometric property, thus we obtain a sufficient condition for the absolute continuity of $\omega$ and $\sigma$.