Finite sphere packings in low and high dimensions

Ji Hoon Chun (TU Berlin)

Jan 20. 2022, 16:30 — 17:10

I present two complementary problems on finite sphere packings in Euclidean space. The Sausage Conjecture (L. Fejes Tóth) states that in dimensions d ≥ 5, the densest packing of any finite number of spheres in R^d occurs if and only if the spheres are all packed in a line, i.e., a sausage. The Sausage Catastrophe (J. Wills) is the observation that in d = 3 and 4, the densest packing of n spheres is a sausage for small n and jumps to a full-dimensional packing for large n without passing through any intermediate dimensions. I will discuss the progress made in the literature including the result that the Sausage Conjecture is true for all d ≥ 42 (Betke and Henk). Furthermore, I will present some initial improvements to the existing partial results of both problems as well as mention some future research directions. 

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)