Discrete Ricci curvature and flows

We introduce various discrete Ricci curvature notions under the unified framework of gradient estimates for the heat equation. We discuss the corresponding notions of Ricci flows. Assuming Ricci lower bounds, we prove eigenvalue estimates, diameter bounds, concentration of measure, Li-Yau inequalities and Log-Sobolev inequalities.

Date and time info
Friday 15.45-17.15

Keywords
Ricci curvature, Markov chains, Gradient estimates

Prerequisites
Basic linear algebra and analysis should be sufficient

Language
English