Geometry and arithmetic of sphere packings

Members' Seminar
Topic:Geometry and arithmetic of sphere packings
Speaker:Alex Kontorovich
Affiliation:Rutgers University
Date:Monday, October 23
Time/Room:2:00pm - 3:00pm/S-101
Video Link:https://video.ias.edu/membsem/2017/1023-AlexKontorovich

We introduce the notion of a "crystallographic sphere packing," which generalizes the classical Apollonian circle packing. Tools from arithmetic groups, hyperbolic geometry, and dynamics are used to show that, on one hand, there is an infinite zoo of such objects, while on the other, there are essentially finitely many of these, in all dimensions. No familiarity with any of these topics will be assumed.