Magic functions for sphere packings and energy minimization.

Speaker(s) Maryna Viazovska EPFL - Ecole Polytechnique Fédérale de Lausanne
Date 23 September 2021 – 14:00 to 15:00
Venue INI Seminar Room 1
Session Title Magic functions for sphere packings and energy minimization.
Event [OOEW02] The unity of mathematics: A conference in honour of Sir Michael Atiyah
Abstract

In this lecture we will show  that the E8 and Leech lattices minimize energy for a wide class of potential functions. This theorem implies recently proven optimality of E8 and Leech lattices as sphere packings and broadly generalizes it to long-range interactions. The key ingredient of the proof is sharp linear programming bounds. Construction of the optimal auxiliary functions attaining these bounds is based on a new interpolation theorem. This is joint work with Henry Cohn, Abhinav Kumar, Stephen D. Miller, and Danylo Radchenko.

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