Lectures in course MATH-476: Optimal transport

Optimal Transport: Convexity and Geodesics

Explores convexity in optimal transport, focusing on potential energy and geodesics.

Optimal Transport: Introduction and Kantorovich Problem

Introduces the course on optimal transport, covering historical background, concepts of push forward measures, transport maps, and the Kantorovich problem.

Isoperimetric Inequality: Optimal Transport

Explores the isoperimetric inequality and its application in optimal transport, discussing properties of optimal maps and quality cases.

Optimal Transport: Convexity and Inequalities

Explores optimal transport, emphasizing convexity properties and inequalities in compact sets.

Geodesic Convexity: Theory and Applications

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Optimal Transport: Theory and Applications

Covers the theory and applications of optimal transport, focusing on infimal convolution and Kantorovich potentials.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Optimal Transport: Gradient Flows in Rd

Explores optimal transport and gradient flows in Rd, emphasizing convergence and the role of Lipschitz and Picard-Lindelöf theorems.

Optimal Transport: Gradient Flows

Explores optimal transport, gradient flows, the implicit Euler scheme, and the heat equation in the context of Dirichlet energy functional.

Optimal Transport: Prokhorov Theorem

Covers the Prokhorov Theorem in Optimal Transport, emphasizing support sets and optimality conditions.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Optimal Transport: Cyclically Monotone Sets

Covers cyclically monotone sets in optimal transport theory and their properties.

Optimal Transport: Rockafellar Theorem

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Optimal Transport: In-Depth Evaluation

Explores optimal transport theory with a focus on heat equations and Wasserstein distance.

Optimal Transport: Convex Analysis

Explores optimal transport and convex analysis, emphasizing convex functions and their applications.

Optimal Transport: Theory and Applications

Explores optimal transport theory, transport maps, entropy, and their practical implications in mathematical optimization.

Optimal Transport: Kantorovich Duality

Covers optimal transport and Kantorovich duality in real-life distribution problems.

Optimal Transport: Theory and Applications

Explores Lagrange multipliers, minimax theorems, and convex subsets in optimal transport theory.

Optimal Transport: Brenier's Theorem

Discusses Brenier's theorem in optimal transport and the uniqueness of the optimizer.

Optimal Transport: Theory and Applications

Explores the theory of optimal transport, focusing on Lipschitz functions and uniqueness of solutions.