2016/03/31 by Henry Cohn, Abhinav Kumar, Stephen D. Miller +2 · 8 citations
Computer Science · Mathematics · #Circle packing #Combinatorics #Digital Image Processing Techniques #Dimension (graph theory) #Function (biology) #Geometry #Lattice (music) #Linear programming #Mathematical Approximation and Integration #Mathematical optimization #Mathematics #Packing problems #Point processes and geometric inequalities #SPHERES #Sphere packing #math.MG #math.NT
paper · pdf · doi:10.4007/annals.2017.185.3.8
published as Annals of Mathematics 185 (2017), 1017-1033 · 17 pages
openalex publication_date 2017/02/24 · arxiv created 2017/08/28 · arxiv updated 2017/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.