Three point bounds for sphere packing

Andrew Salmon (MIT, Cambridge)

Jan 18. 2022, 16:30 — 17:10

We define three-point bounds for sphere packing that refine the linear programming bound, and we compute these bounds numerically using semidefinite programming by choosing a truncation radius for the three-point function. As a result, we obtain new upper bounds on the sphere packing density in dimensions 4 through 7 and 9 through 12.  We also give a different three-point bound for lattice packing and conjecture that this second bound is sharp in dimension 4.

Joint work with Henry Cohn and David de Laat

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Optimal Point Configurations on Manifolds (Workshop)
Christine Bachoc (U Bordeaux)
Henry Cohn (Microsoft, Redmond)
Peter Grabner (TU Graz)
Douglas Hardin (Vanderbilt U, Nashville)
Edward Saff (Vanderbilt U, Nashville)
Achill Schürmann (U of Rostock)
Robert Womersley (UNSW, Sydney)