Mathematical Sciences Research Institute

Home » Workshop » Schedules »  Local to global principles in integral circle packings

Local to global principles in integral circle packings

Recent developments in Analytic Number Theory May 01, 2017 - May 05, 2017

May 05, 2017 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Elena Fuchs (University of California, Davis)
Location: MSRI: Simons Auditorium
  • Apollonian circle packing

  • expander graphs

  • Descartes quadruple

  • quadratic form

  • Apollonian group

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



One of the most spectacular results on arithmetic of Apollonian circle packings is the "almost" local to global principle for curvatures in any given integral Apollonian packing as described by Bourgain-Kontorovich in 2014. The methods in their work, inspired originally by an observation of Sarnak’s in his letter to Lagarias on Apollonian circle packings, apply to a much larger class of circle packings. In this talk, we clarify what "almost" local to global means, and describe what the larger class is, as well as what aspects of the packings in this class seem necessary in order to conclude an "almost" local to global result and how they enter the proof. This is joint work with Stange and Zhang.

28403?type=thumb Fuchs Notes 4.75 MB application/pdf Download
Video/Audio Files


H.264 Video 15-Fuchs.mp4 115 MB video/mp4 rtsp://videos.msri.org/data/000/028/332/original/15-Fuchs.mp4 Download
Troubles with video?

Please report video problems to itsupport@msri.org.

See more of our Streaming videos on our main VMath Videos page.