报告题目 (Title)：Curvature and local matchings of amply regular graphs (amply regular图的曲率和局部图的匹配)
报告人 (Speaker)：刘世平 教授（中国科学技术大学）
报告时间 (Time)：2024年9月13日(周五) 10:00
报告地点 (Place)：腾讯会议 271-962-145
邀请人(Inviter)：杨倩倩
主办部门：金沙威尼斯欢乐娱人城数学系
报告摘要： Bounding the diameter of a distance-regular graph in terms of its intersection numbers is a very important problem. Recently, there are strong interests to bound the diameter via a small initial part of the intersection array (see, e.g., Neumaier-Penjić, Combinatorica 2022). For that purpose, we consider the diameter estimates of a more general class of graphs called amply regular graphs. In differential geometry, a general principle is that the curvature lower bounds at every point of a space leads to a diameter upper bound. In this talk, we will discuss sharp diameter bounds for amply regular graphs derived from estimating the Lin-Lu-Yau curvature of each edge. Calculating the Lin-Lu-Yau curvature often reduces to showing the existence of certain local matching conditions. We will further address a conjecture of Bonini et. al. in 2020 on the curvature of conference graphs. This talk is based on joint works with Xueping Huang, Qing Xia, Kaizhe Chen, and Heng Zhang.
