An introduction to the Bakry-Émery curvature-dimension condition

Abstract: A compact, connected Riemannian manifold with a positive lower bound on the Ricci curvature satisfies several nice properties. Using the heat flow on a compact Riemannian manifold as motivation, we will discuss the Bakry-Émery curvature-dimension condition, which adapts the notion of a Ricci curvature lower bound to Markov processes. If time permits, we will provide a proof sketch of its relationship with Poincaré and log-Sobolev inequalities.