Mathematics Colloquium

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Ricci Curvature and Optimal Transport

Speaker: Elia Brué, Bocconi University

Location: Warren Weaver Hall 1302

Date: Monday, March 9, 2026, 3:45 p.m.

Synopsis:

The study of the geometric and topological constraints imposed by lower Ricci curvature bounds is a classical and far-reaching theme in Riemannian geometry. We survey a nonsmooth approach to this subject, beginning with Cheeger–Colding’s theory of Ricci limit spaces and continuing with the optimal transport formulation of curvature, culminating in the RCD(K,N) theory. We conclude with applications, including recent results on tangent cones of 4-manifolds with nonnegative Ricci curvature.