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This Arbeitsgemeinschaft was devoted to recent developments in optimal transport with emphasis on links and applications to geometry. The topics reached from the origin of optimal transport as a variational problem, where one minimizes a transportation cost when transporting one density into another, over the introduction of a metric on the space of probability measures, leading to the Wasserstein-space and convex funtionals on it, to the connection between Ricci-curvature and the optimal mass transport problem.
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Felix Otto, Karl-Theodor Sturm, Arbeitsgemeinschaft: Optimal Transport and Geometry. Oberwolfach Rep. 6 (2009), no. 2, pp. 983–1018