Mini-course on Optimal Transport and High-Dimensional Probability (with Sinho Chewi)
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Density functional theory and multi-marginal optimal transport: Introduction
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Sectional curvature, matrix displacement convexity, and intrinsic dimensional functional inequalities
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A dynamical formulation of multi-marginal optimal transport
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Optimal transport maps, majorization, and log-subharmonic measures
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The Brownian and Poisson transport maps
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Matrix displacement convexity along density flows
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Transport and renormalization via probabilistic Hessian estimates
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The extremals of Stanley’s inequalities for partially ordered sets
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Renormalization groups, transport maps, and multiscale Bakry-Emery criteria
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Transportation along Langevin semigroups
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The Brownian transport map
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The Extremal Structures of the Alexandrov-Fenchel Inequality
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Quantum graphs, convex bodies, and a century-old problem of Minkowski
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