Japanese Journal of Mathematics

, Volume 9, Issue 1, pp 69-97

First online:

Apollonian circle packings: dynamics and number theory

  • Hee OhAffiliated withMathematics Department, Yale UniversityKorea Institute for Advanced Study Email author 

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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.

Keywords and phrases

Apollonian circle packing expander thin group geometrically finite group equidistribution

Mathematics Subject Classification (2010)

11N45 37F35 22E40