Chengfei Xie, On the packing densities of superballs in high dimensions

The sphere packing problem asks for the densest packing of nonoverlapping equal-sized balls in the space. This is an old and difficult problem in discrete geometry. In this talk, we give a new proof for the result that for $ 1<p<2 $, the translative packing density of superballs (a generalization of $\ell^p$ balls) in $\mathbb{R}^n$ is $\Omega(n/2^n)$.
This is joint work with Gennian Ge.