Curvature, diameter and eigenvalues of amply regular graphs
数学专题报告
报告题目(Title)：Curvature, diameter and eigenvalues of amply regular graphs
报告人(Speaker)：刘世平 教授（中国科学技术大学）
地点(Place)：腾讯会议ID：980 008 3315
时间(Time)：2023年1月12日(周四), 14：00-15：00
邀请人(Inviter)：赵亮
报告摘要
In differential geometry, a general principle is that the information about curvature at every point leads to diameter and eigenvalue bounds. Analogous results have been established for graphs. In this talk, we elaborate the point that the local regularity conditions of an amply regular graph play a role very similar to curvature. We will discuss sharp diameter and eigenvalue bounds for amply regular graphs derived from estimating the Lin-Lu-Yau curvature of each edge. Our curvature estimates involve new ideas relating discrete Ricci curvature with local matching properties. This talk is based on joint works with Xintian Li, Xueping Huang, and Qing Xia.
主讲人简介
刘世平，中国科学技术大学数学科学学院教授，博士生导师，曾入选国家青年人才计划。主要研究兴趣集中在离散几何分析领域，例如由黎曼几何和整体分析中的结果和方法所引导的离散空间相应问题；图论或理论计算机科学等离散数学领域本身所关心且有希望用几何分析方法来解决的问题；在离散空间上发展新方法新结果后应用到连续空间上揭示新发现等。论文发表在Adv. Math.，Crelle's Journal，Mathematical Research Letters等优秀数学期刊。
