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Seminars

Seminar
FIELD Math:Analysis
DATE January 23 (Thu), 2020
TIME 17:00-18:00
PLACE 1423
SPEAKER Oh, Byung-Geun
HOST Kang, Nam-Gyu
INSTITUTE 한양대학교
TITLE Some criteria for circle packing types and combinatorial Gauss-Bonnet theorem
ABSTRACT In a paper from 1995, He and Schramm developed some tools for determining whether a given circle packing is parabolic or hyperbolic; i.e., whether it fills the whole plane or not. They proved in the same paper many criteria for circle packing parabolicity or hyperbolicity, but there were two criteria, according to He and Schramm, with a wide gap.

In this talk we will discuss about this gap. In fact, there was a conjecture by He and Schramm, which was later proved by Repp in 2001, that deals with this gap, but our results could fill the gap much further. We will also talk about layered circle packings, and our main method for these problems, called the combinatorial Gauss-Bonnet theorem involving boundary turns.
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