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

Abstract

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.

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

Fuchs

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