丘成桐中心几何与方程讨论班
SEU Yau Center Geometry and PDE Seminar
刘世平 教授学术报告
Title: Curvature, diameter and eigenvalues of amply regular graphs
Speaker: Prof. Shiping Liu（刘世平）
Affiliation：University of Science and Technology of China （中国科学技术大学）
Time: 14:00-15:00, May 18th (Thur.), 2023 (GMT+8)
Venue: Room 1502, Yifu Architecture Building, Sipailou Campus of Southeast University, Nanjing
（东南大学四牌楼校区逸夫建筑馆丘成桐中心1502室）
Inviter: Yi Li（李逸）
Abstract:
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.Speaker:
刘世平，中国科学技术大学数学科学学院副院长，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。