Speaker: 刘世平 （中国科学技术大学）

Venue: B924

Time: 2017年11月03日 15:00-16:00

Title: Discrete Bonnet-Myers theorem and rigidity properties of hypercubes

Abstract: It is a general principle in the study of geometry to derive global properties from information at every local of a space. We will discuss such an approach on discrete structures in this talk. It is natural to ask whether a graph is a hypercube if the 2-ball of each vertex is isomorphic to that of a vertex in a hypercube. It turns out that this is not true and we need curvature-like restrictions. We will present a discrete Bonnet-Myers theorem and discrete Cheng type rigidity theorems. The discrete curvature notion we use is Bakry-Emery curvature dimension inequalities.

This is based on joint works with Florentin Muench (Harvard/Potsdam), Norbert Peyerimhoff (Durham), and Christian Rose (Chemnitz).