
Ricci Curvature of Directed Graphs
OTHER MATHEMATICS DEPARTMENT EVENTS: MATH TABLE
This talk will explore the notion of curvature on undirected and directed graphs using concepts from discrete differential geometry and introduce the exciting applications of graph curvature in geometric machine learning and network science. We will focus on a local notion of curvature called Ricci curvature and how it can be generalized to metric spaces endowed with probability measures or random walks as done with Ollivier Ricci curvature. We will then discuss recent research in defining Ollivier Ricci curvature on undirected and directed graphs using optimal transport and fundamental differential geometry, and finally the mathematical challenges involved with capturing discrete local curvature when directionality constraints are present.