Un Mokameeting aura lieu le mercredi 24 novembre 2021 à 14h00.
Nous aurons le plaisir d’écouter deux exposés, l’un de Michael Goldman (LJLL, Paris 7), l’autre de Bernhard Schmitzer (Université de Göttingen).
Exposé de Michael Goldman
Titre : On recent progress on the optimal matching problem
Résumé : The optimal matching problem is a classical random combinatorial problem which may be interpreted as an optimal transport problem between random measures. Recent years have seen a renewed interest for this problem thanks to the PDE ansatz proposed in the physics literature by Caracciolo and al. and partially rigorously justified by Ambrosio-Stra-Trevisan. In this talk I will show how this ansatz combined with subadditivity may be used to give information both on the optimal cost and on the structure of the optimal transport map at various scales. This is based on joint works with L. Ambrosio, M. Huesmann, F. Otto and D. Trevisan.
Exposé de Bernhard Schmitzer
Titre : Domain decomposition for optimal transport
Résumé : Large optimal transport problems can be approached in a distributed way via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Benamou proved convergence to the global minimizer in the setting of Brenier’s theorem under suitable regularity assumptions on the decomposition. We show that with entropic regularization global convergence becomes much easier to prove and present a corresponding computationally efficient algorithm. To obtain a better understanding of the method we also discuss its limit behaviour in the regime of infinitesimally small decompositions.
