Japanese Journal of Mathematics

, Volume 9, Issue 1, pp 69–97

Apollonian circle packings: dynamics and number theory


DOI: 10.1007/s11537-014-1384-6

Cite this article as:
Oh, H. Jpn. J. Math. (2014) 9: 69. doi:10.1007/s11537-014-1384-6


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 packingexpanderthin groupgeometrically finite groupequidistribution

Mathematics Subject Classification (2010)


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