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Thin groups: arithmetic and geometric viewpoints

Introductory Workshop: Geometric and Arithmetic Aspects of Homogeneous Dynamics February 02, 2015 - February 06, 2015

February 06, 2015 (10:10 AM PST - 11:10 AM PST)
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

14174

Abstract

In the past decade, substantial progress has been made in several beautiful arithmetic problems connected to thin groups: Apollonian packings, Zaremba's conjecture, and so on.  This progress was made possible by a series of developments, in particular the Affine Sieve of Bourgain-Gamburd-Sarnak from a decade ago.  In this talk we will focus on the arithmetic of Apollonian packings, and then move on to consider thin groups in their own right, apart from arithmetic applications.  Specifically, we will discuss how hyperbolic geometric methods have shed light on thinness of certain monodromy groups of hypergeometric equations, and how one might go about distinguishing thin groups from their non-thin counterparts in general.

Supplements
23256?type=thumb Fuchs Notes 312 KB application/pdf Download
Video/Audio Files

14174

H.264 Video 14174.mp4 353 MB video/mp4 rtsp://videos.msri.org/data/000/022/841/original/14174.mp4 Download
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