Sphere Packings and Arithmetic

Department of Mathematics Colloquium

Meeting Details

For more information about this meeting, contact Kristin Berrigan, Stephanie Geyer, Sergei Tabachnikov, Dmitri Burago, Alberto Bressan, Nigel Higson.

Speaker: Alex Kontorovich, Rutgers University

Abstract: We will discuss recent work on "crystallographic" sphere packings (defined in work with Nakamura), and the subclass of "superintegral" such. (A quintessential example is the classical Apollonian Circle Packing.) These exist in finitely many dimensions, and in fact in finitely many commensurability classes in each dimension. This is a consequence of the Arithmeticity Theorem, that such packings come from arithmetic hyperbolic reflection groups.

Room Reservation Information

Room Number: 114 McAllister

Date: 09/19/2019

Time: 3:30pm - 4:30pm