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Introduction to optimal transport theory - lecture 2

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Auteurs : Santambriogio, Filippo (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : Optimal transport, a mathematical theory which developed out of a problem raised by Gaspard Monge in the 18th century and of the reformulation that Leonid Kantorovich gave of it in the 20th century in connection with linear programming, is now a very lively branch of mathematics at the intersection of analysis, PDEs, probability, optimization and many applications, ranging from fluid mechanics to economics, from differential geometry to data sciences. In this short course we will have a very basic introduction to this field. The first lecture (2h) will be mainly devoted to the problem itself: given two distributions of mass, find the optimal displacement transforming the first one into the second (studying existence of such an optimal solution and its main properties). The second one (2h) will be devoted to the distance on mass distributions (probability measures) induced by the optimal cost, looking at topological questions (which is the induced topology?) as well as metric ones (which curves of measures are Lipschitz continuous for such a distance? what can we say about their speed, and about geodesic curves?) in connection with very natural PDEs such as the continuity equation deriving from mass conservation.

Keywords : optimal transport; convex duality; Wasserstein distances; continuity equation

Codes MSC :
35-XX - Partial differential equations
49J45 - Problems involving semicontinuity and convergence
49Q22 - Optimal transportation

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 01/08/2022
    Date de captation : 19/07/2022
    Sous collection : Research School
    arXiv category : Optimization and Control ; Analysis of PDEs
    Domaine : Analysis and its Applications ; Control Theory & Optimization ; PDE
    Format : MP4 (.mp4) - HD
    Durée : 02:03:16
    Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2022-07-19_Santambriogio_2.mp4

Informations sur la Rencontre

Nom de la rencontre : CEMRACS: Transport in Physics, Biology and Urban Traffic / CEMRACS: Transport en physique, biologie et traffic urbain
Organisateurs de la rencontre : Franck, Emmanuel ; Hivert, Helene ; Latu, Guillaume ; Leman, Hélène ; Maury, Bertrand ; Mehrenberger, Michel ; Navoret, Laurent
Dates : 18/07/2022 - 22/07/2022
Année de la rencontre : 2022
URL Congrès : http://smai.emath.fr/cemracs/cemracs22/s...

Données de citation

DOI : 10.24350/CIRM.V.19940703
Citer cette vidéo: Santambriogio, Filippo (2022). Introduction to optimal transport theory - lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19940703
URI : http://dx.doi.org/10.24350/CIRM.V.19940703

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