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Sphere Packings and Arithmetic

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Alex Kontorovich
Rutgers University
Thu, 2018-07-05 14:00 - 14:50
MPIM Lecture Hall

We define a general class of "crystallographic" sphere packings, and study the subclass of "superintegral" such. We prove an "arithmeticity" theorem, connecting these to the theory of hyperbolic arithmetic reflection lattices. As a consequence, superintegral packings only exist in finitely many dimensions, and in fact in finitely many commensurability classes, in principle allowing for a complete classification.

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