**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. In the talk I will present some of the theory of circle packings and random walks and discuss some of the ideas used in the proof. Joint work with Ori Gurel-Gurevich.

Video of the talk can be found here:

https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=c1aa8b1a-72eb-4487-a2ee-abb200aa0fb9

**Zoom meeting info:**

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Meeting ID: 999 8461 2159

Password: 3c99b6

## Date:

Tue, 05/05/2020 - 12:00 to 13:00