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MATH-476: Optimal transport

Summary

The first part is devoted to Monge and Kantorovitch problems, discussing the existence and the properties of the optimal plan. The second part introduces the Wasserstein distance on measures and develops applications of optimal transport to PDEs, functional/geometric inequalities, traffic models.

Lectures

Instructor

Xavier Fernandez-Real Girona

Official source

https://edu.epfl.ch/coursebook/en/optimal-transport-MATH-476

Moodle Page

http://go.epfl.ch/MATH-476

About this result

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Summary

Lectures

Instructor

Xavier Fernandez-Real Girona

Official source

https://edu.epfl.ch/coursebook/en/optimal-transport-MATH-476

Moodle Page

http://go.epfl.ch/MATH-476

About this result

Lectures in this course (26)

Optimal Transport: Introduction and Kantorovich Problem Log in to Mediaspace to watch this video

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

Isoperimetric Inequality: Optimal Transport Log in to Mediaspace to watch this video

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

Optimal Transport: Brenier's Theorem Log in to Mediaspace to watch this video

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

Optimal Transport: Theory and Applications Log in to Mediaspace to watch this video

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

Optimal Transport: Stability and Monotonicity Log in to Mediaspace to watch this video

Explores the stability and monotonicity of optimal transport plans and their practical implications.

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