Analysis Seminar

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New Lower Bounds for Sphere Packing

Speaker: Marcelo Campos, Cambridge University & IMPA

Location: Warren Weaver Hall 1302

Date: Tuesday, November 19, 2024, 11 a.m.

Synopsis:

In this talk I'll show the existence of a packing of identical spheres in \(\mathbb{R}^d\) with density \((1-o(1))\frac{d\log d}{2^{d+1}}\) as \(d\to \infty\). This improves the best known asymptotic lower bounds for sphere packing density. The proof uses a connection with graph theory and a new result about independent sets in graphs which is proved probabilistically.

This is joint work with Matthew Jenssen, Marcus Michelen and Julian Sahasrabudhe.

Notes:

Special Analysis Seminar