报告题目: Bakry-/'Emery curvature functions of graphs

报告人：David Cushing, Durham University, UK

时间：3月10日周五下午2:30-3:30
地点：管研楼1518
摘要: We study the Bakry-/'Emery curvature function $/K_{G,x}:(0,/infty]/to /mathbb{R}$ of a vertex $x$ in a locally finite graph $G$ systematically.Here $/K_{G,x}(/N)$ is defined as the optimal curvature lower bound $/K$ in the Bakry-/'Emery curvature-dimension inequality $CD(/K,/N)$ that $x$ satisfies. We prove the curvature functions of the Cartesian product of two graphs $G_1,G_2$ equal an abstract product of curvature functions of $G_1,G_2$. We relate the curvature functions of $G$ with various spectral properties of (weighted) graphs constructed from local structures of $G$. We we will also demonstrate a piece of interactive software for calculating curvature.

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