## Ricci-flat graphs

- March 26, 2012
- 3:50 p.m.
- LeConte 312

## Abstract

The Ricci curvature plays a very important role on geometric analysis on Riemannian manifolds. In 2009, Ollivier gave a notion of coarse Ricci curvature of Markov chains valid on arbitrary metric spaces. His definition of coarse Ricci curvature was adapted by Lin-Lu-Yau so that it is more suitable for graphs. A graph is called Ricci-flat if Ricci curvatures varnish on all edges. In this talk, we classify connected Ricci-flat graphs with girth at least 5.

(Joint work with Yong Lin and S.-T. Yau)