北航微分几何讨论班（2021秋第10讲）

题目：Discrete Ricci curvatures of graphs: The computation side

报告人：刘世平 教授（中国科技大学）

时间：2021年11月16日 10:00-11:00

腾讯会议会议号：982 7145 2005

摘要：We concern in this talk the computation of Bakry-\'Emery curvature and Ollivier/Lin-Lu-Yau curvature of graphs. It is recently discovered that computing Bakry-\'Emery curvatures at a vertex of a graph reduces to calculating the smallest eigenvalue of a so-called curvature matrix and its rank-one perturbations. This provides an analogue of the basic fact in Riemannian geometry that the optimal Ricci curvature lower bound at a point is the smallest eigenvalue of the Ricci curvature tensor. For Ollivier/Lin-Lu-Yau curvature of graphs, it is known that the computation reduces to certain matching problem. We will particularly discuss the discrete curvatures of graphs with local regularities. While the curvatures of such graphs with girth at least 4 are relatively clear, the case of girth 3 is rather mysterious. This talk is based on joint works with David Cushing, Supanat Kamtue, Riikka Kangaslampi, Norbert Peyerimhoff and Xin-Tian Li.

报告人简介：刘世平，现为中国科技大学特任教授，2016年入选国家级青年人才计划，研究方向为几何分析、离散几何等，已经在Crelles, Adv. Math.，Commun.Anal.Geom.等国际著名数学期刊上发表论文近30篇。

邀请人：张世金