seminar: Ricci curvature and displacement convexity
speaker: Alessio Figalli (ETH Zurich)abstract: Recent research activity by Lott, Villani, Sturm, Von Renesse has been devoted to study the geometry of Riemannian manifolds and, more in general, length spaces, through the geometry of their associated Wasserstein space of probability measures. In particular, it was found that lower bounds on the Ricci curvature tensor can be recast in terms of convexity properties of certain nonlinear functionals defined on spaces of probability measures. I will first recall the notion of measured length space having Ricci curvature bounded from below, using optimal transport and displacement convexity. Then, I will present a recent result obtained in collaboration with C. Villani where we solve a natural problem in this field by establishing the equivalence of several formulations of convexity properties.
timetable:
Wed 15 Nov, 16:00 - 16:55, Aula Dini
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