Large scale curvature of graphs

Speaker: Gabor Lippner (Northeastern, USA)

Abstract:

I will explain the Bakry-Emery framework for understanding curvature of graphs via the so-called curvature-dimension inequalities, what kind of properties of the graph (spectrum, random walk, etc) can they be used to understand, and what their limitations are.

Then I will define a hybrid between Ollivier and Bakry-Emery curvature on graphs with dependence on a variable neighborhood, that overcomes one of the major limitations of curvature-dimension inequalities, but still allows to prove gradient estimates similar to the ones obtained from Bakry-Emery curvature.