## Mathematical Computer Science Seminar

Will Perkins

UIC

Sphere packings and kissing numbers in high dimensions via hard core models

**Abstract:**We improve the classic Chabauty-Shannon-Wyner lower bound on the kissing number of Euclidean space by a factor linear in the dimension. The proof is based on analyzing a "hard cap" model related to the hard core lattice gas from statistical physics. The proof technique also applies to sphere packings and to independent sets in triangle-free graphs. I will use the connection with independent sets in graphs to describe some plausible scenarios for the densest sphere packings and kissing configurations in high dimensions. Based on joint work with Matthew Jenssen and Felix Joos.

Monday September 17, 2018 at 3:00 PM in 427 SEO