## 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.

기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209