Coarse Ricci Curvature of Hypergraphs

Abstract: There are several notions of (lower bound of) Ricci curvature on discrete spaces. I will give a new notion of Ricci curvature on hypergraphs related to the Lin- Lu-Yau’s coarse Ricci curvature on graphs (LLY curvature for short). The definition of LLY curvature defined by using the Markov chain on vertex set on graph. Since the Laplacian of hypergraph is nonlinear, it is difficult to define Ricci curvature on hypergraphs in the same way as LLY one. In my talk, I explain how to overcome such difficulties and tell the geometric consequences of assuming lower bound of Ricci curvature. These are based on two joint works with M.IkedaY.Takai-T.Uehara, and with E.Matsumoto.

Mathematics

Audience: researchers in the topic

IUT Mathematics Research Seminars (IMRS)

Series comments: All researchers are welcomed!