Title: Random walks on planar graphs
Abstract: We will discuss several results relating the behavior of a random walk on a planar graph and the geometric properties of a nice embedding of the graph in the plane (e.g. a circle packing of the graph). An example of such a result is that for a bounded degree graph, the simple random walk is recurrent if and only if the boundary of the nice embedding is a polar set (that is, Brownian motion misses it almost surely).
No prior knowledge about random walks, circle packings or Brownian motion is required.
Based of joint works with Omer Angel, Martin Barlow, Daniel Jerison, Asaf Nachmias, Matan Seidel and Juan Souto.