Course

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, gradient flows.

Lectures

Instructor

Maria Colombo

Teaching & PhD PhD Students Roberto Colombo, Antonio Tirotta, Carl Johan Peter Johansson, Giulia Mescolini Past EPFL PhD Students Luigi De Rosa, Silja Noëmi Aline Haffter, Massimo Sorella Courses Analysis IV - Lebesgue measure, Fourier analysis MATH-205 Learn the basis of Lebesgue integration and Fourier analysis Topics on the Euler and Navier-Stokes equations MATH-647 This topics course focuses on recent and classical fundamental results on the Euler and Navier-Stokes equa

Official source

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

Moodle Page

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

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Summary

Lectures

Instructor

Maria Colombo

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: Convexity and Geodesics

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

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: 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.

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