Sphere Packing Bounds Via Spherical Codes

Analysis Seminar
Topic:Sphere Packing Bounds Via Spherical Codes
Speaker:Henry Cohn
Affiliation:Microsoft Research New England/MIT
Date:Tuesday, January 22
Time/Room:4:30pm - 5:30pm/S-101
Video Link:https://video.ias.edu/1213/analysis/0122-HenryCohn

We develop a simple geometric variant of the Kabatiansky-Levenshtein approach to proving sphere packing density bounds. This variant gives a small improvement to the best bounds known in Euclidean space (from 1978) and an exponential improvement in hyperbolic space. Furthermore, we show how to achieve the same results via the Cohn-Elkies linear programming bounds, and we formulate a few problems in harmonic analysis that could lead to even better bounds. This is joint work with Yufei Zhao.