Sergey Norin, Asymptotic dimension of intersection graphs

The notion of asymptotic dimension of metric spaces, introduced by Gromov, describes their large-scale behaviour. Asymptotic dimension of graph families has been recently studied, in particular, by Bonamy et al. who proved that the asymptotic dimension of proper minor-closed graph families is at most two.

We will discuss nerve-type theorems for asymptotic dimension. In particular, we show that the asymptotic dimension of intersection graphs of balls and spheres in $\mathbb{R}^d$ is at most $d+1$.

Based on joint work with Zdeněk Dvořák and with Chun-Hung Liu.