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Drunks in an unfair world: Elliptic measures and the geometry of the domains

Zihui Zhao
Thursday, April 26, 2018 - 2:30pm to 3:20pm
PDL C-36
Abstract: Given a bounded domain \Omega, the harmonic measure \omega is a probability measure on \partial\Omega and it characterizes where a Brownian traveller 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 \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.
This talk is a preparation for my thesis defense!
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