Three-point bounds for sphere packing

With David de Laat (Delft)

Three-point bounds for sphere packing

The sphere packing problems asks for the densest packing of Euclidean space by congruent balls that do not intersect in their interiors. The Cohn-Elkies linear programming bound can be used to obtain upper bounds on the optimal density and has been used by Viazovska and others to show the E_8 root lattice and Leech lattice configurations in dimensions 8 and 24 are optimal. In other dimensions (except for dimensions 1 and 2) the linear programming bound is not expected to be sharp and currently only small improvements on this bound are known. In this talk I will discuss new three-point bounds for sphere packing and lattice sphere packing that we use to obtain larger improvements.

Joint work with Henry Cohn and Andrew Salmon

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