, Volume 9, Issue 1, pp 69-97
Date: 15 Feb 2014

Apollonian circle packings: dynamics and number theory

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Abstract

We give an overview of various counting problems for Apollonian circle packings, which turn out to be related to problems in dynamics and number theory for thin groups. This survey article is an expanded version of my lecture notes prepared for the 13th Takagi Lectures given at RIMS, Kyoto in the fall of 2013.

Communicated by: Toshiyuki Kobayashi
This article is based on the 13th Takagi Lectures that the author delivered at Research Institute for Mathematical Sciences, Kyoto University on November 16 and 17, 2013.