Geometry and arithmetic of sphere packings

Geometry and arithmetic of sphere packings - Alex Kontorovich

Alex Kontorovich
Rutgers University
October 23, 2017
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.
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