The sphere packing problem in dimension 24
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In this article, it was shown that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing.Abstract:
Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particular, we find an optimal auxiliary function for the linear programming bounds, which is an analogue of Viazovska's function for the eight-dimensional case.read more
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References
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TL;DR: A program to prove the Kepler conjecture on sphere packings is described and it is shown that every Delaunay star that satisfies a certain regularity condition satisfies the conjecture.
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