Japanese Journal of Mathematics

, Volume 9, Issue 1, pp 69–97 | Cite as

Apollonian circle packings: dynamics and number theory



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 


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Copyright information

© The Mathematical Society of Japan and Springer Japan 2014

Authors and Affiliations

  1. 1.Mathematics DepartmentYale UniversityNew HavenUSA
  2. 2.Korea Institute for Advanced StudySeoulRepublic of Korea

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