### A new lower bound for sphere packing

Combinatorics Seminar

16th April 2024, 11:00 am – 12:00 pm

Fry Building, 2.04

The classical sphere packing problem asks: what is the densest possible arrangement of identical, non-overlapping spheres in $\mathbb{R}^d$? I will discuss a recent proof that there exists a sphere packing with density at least

(1-o(1))\frac{d \log d}{2^{d+1}}.

This improves upon previous bounds by a factor of order $\log d$ and is the first improvement by more than a constant to Rogers' bound from 1947. This is joint work with Marcelo Campos, Marcus Michelen and Julian Sahasrabudhe.

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