Neighborhood graphs, Ricci curvature and optimal transport on graphs
Ricci curvature is a notion originally introduced in Riemannian geometry. Ricci curvature is intimately related to eigenvalue bounds, regularity results in geometric analysis, and recurrence of stochastic processes. It admits various characterization in terms of volume growth, optimal transport, or coupling between stochastic processes. Some of these characterizations can be formulated in more abstract ways, so that they apply to spaces more general than Riemannian manifolds. In this talk, I shall explore this scheme for graphs and connect with ideas and tools from graph theory. In particular, eigenvalue estimates for graphs will be presented.
The talks represents joint work with Frank Bauer, Bobo Hua, and Shiping Liu.