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 $\mathrm{\Omega }(n/2^n)$.
This is joint work with Gennian Ge.