2020
May
05

# Dynamics Lunch: Or Landesberg: "Ends of hyperbolic three manifolds and dynamics of horospherical foliations"

12:00pm to 1:00pm

**Abstract:**A circle packing is a canonical way of representing a planar graph. There is a deep connection between the geometry of the circle packing and the proababilistic property of recurrence/transience of the simple random walk on the underlying graph, as shown in the famous He-Schramm Theorem. The removal of one of the Theorem's assumptions - that of bounded degrees - can cause the theorem to fail. However, by using certain natural weights that arise from the circle packing for a weighted random walk, (at least) one of the directions of the He-Schramm Theorem remains true.