00:00:00 / 00:00:00

Introduction to optimal transport theory - lecture 2

De Filippo Santambriogio

Apparaît dans la collection : CEMRACS: Transport in Physics, Biology and Urban Traffic / CEMRACS: Transport en physique, biologie et traffic urbain

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.

Informations sur la vidéo

Bibliographie

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow




Inscrivez-vous

  • Mettez des vidéos en favori
  • Ajoutez des vidéos à regarder plus tard &
    conservez votre historique de consultation
  • Commentez avec la communauté
    scientifique
  • Recevez des notifications de mise à jour
    de vos sujets favoris
Donner son avis