Speaker: Giulio Tiozzo from University of Toronto
Abstract: The Poisson boundary of a random walk on a group is a measure-theoretic object that, as Furstenberg realized, captures the space of bounded harmonic functions on the group. On the other hand, often in geometric group theory and topology we have groups that act by isometries on certain spaces (in particular, spaces of negative curvature, in certain sense), and these spaces come equipped naturally with a topological notion of boundary arising from the geometry of the space.
It is a recurring question in this context whether the geometric boundary can be identified with the Poisson boundary. In this mini-course, we will study random walks on groups with hyperbolic properties (in particular, hyperbolic groups and mapping class groups) and show that, under a finite entropy assumption, the Poisson boundary coincides with the geometric boundary. A central topic that we will discuss is the entropy theory of random walks on groups.
Time: July 28, 29, 30, 31, 4-5 pm China time
Zoom Meeting ID: 961 4984 8773 (Passcode: 381322)
English 
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