Discrete Curvature in Graphs: Flows, Structure, and Topology
演讲者
时间
2026年11月09日 15:00 至 16:00
地点
A3-4-301
线上
Zoom 928 682 9093
(BIMSA)
摘要
This report summarizes my recent collaborative work exploring the role of discrete curvature in graphs across three interconnected aspects. First, regarding geometric flows, I will discuss our results on the convergence of the inverse-weight Lin-Lu-Yau Ricci flow on finite trees towards discrete Einstein metrics. Second, from the perspective of structural graph theory, I present our investigation which connects positive Lin-Lu-Yau curvature to global constraints in K_{2,t}-minor-free graphs. Finally, in the realm of topology, I will introduce our sharp curvature threshold result for GLMY path homology, which helps characterize the survival of topological features. Together, these works attempt to show that discrete curvature can serve as a useful unifying language connecting dynamics, structures, and topology. (Those are based on joint work with Yong Lin, Bobo Hua, Shing-Tung Yau, Jingyan Li, Zixia Song, and Xiaonan Liu.)