Ricci curvature; From Smooth geometry to network analysis (I)

In this seminar, I am going to talk mostly about Ollivier (Coarse) Ricci curvature in metric measure spaces and specifically graphs. Before coming to that point, I describe some intuitions behind this notion which comes from ricci curvature in Riemannian manifolds. Although as one of the discrete generalizations of ricci curvature , Ollivier type keeps fewer properties of Riemannian manifolds , it is somewhat simpler to present and has wide range of examples. This curvature, as an edge-based measure, is a part of relatively new approach for analyzing networks and can encode some important properties of the network.

This seminar is a requisitory introduction of an ongoing project under the supervision of Professor Jost.