Séminaire de Géométrie Algorithmique et Combinatoire

Le Séminaire de Géométrie Algorithmique et Combinatoire vise à regrouper des exposés dans ce domaine au sens le plus large, et dans les disciplines connexes en mathématiques et informatique. Il est ouvert à tous les chercheurs et étudiants intéressés. Les exposés sont destinés à un public large.

Il se tient un jeudi par mois, de 14h à 17h, à l'Institut Henri Poincaré à Paris (plan d'accès), en salle 201.

Contact: seminaire [dot-sign] gac [the-funny-at-sign] ens [dot-sign] fr. Pour recevoir les annonces de ce séminaire, envoyer un message à cette adresse avec [inscription] dans le titre.

La liste des exposés passés est disponible ici.


13 oct. 2016
14h Gabriel Peyré CNRS et DMA, École normale supérieure, Paris
Numerical Optimal Transport and Applications
Optimal transport (OT) has become a fundamental mathematical theoretical tool at the interface between calculus of variations, partial differential equations and probability. It took however much more time for this notion to become mainstream in numerical applications. This situation is in large part due to the high computational cost of the underlying optimization problems. There is however a recent wave of activity on the use of OT-related methods in fields as diverse as computer vision, computer graphics, statistical inference, machine learning and image processing. In this talk, I will review an emerging class of numerical approaches for the approximate resolution of OT-based optimization problems. These methods make use of an entropic regularization of the functionals to be minimized, in order to unleash the power of optimization algorithms based on Bregman-divergences geometry. This results in fast, simple and highly parallelizable algorithms, in sharp contrast with traditional solvers based on the geometry of linear programming. For instance, they allow for the first time to compute barycenters (according to OT distances) of probability distributions discretized on computational 2-D and 3-D grids with millions of points. This offers a new perspective for the application of OT in machine learning (to perform clustering or classification of bag-of-features data representations) and imaging sciences (to perform color transfer or shape and texture morphing). These algorithms also enable the computation of gradient flows for the OT metric, and can thus for instance be applied to simulate crowd motions with congestion constraints. This is a joint work with M. Cuturi and J. Solomon.
15h30 Frédéric Chazal INRIA Saclay—Île-de-France
10 nov. 2016
David Coeurjolly CNRS et LIRIS, Université de Lyon
Jean-Marie Mirebeau CNRS et Université Paris-Sud
8 déc. 2016
Gil Kalai Hebrew University of Jerusalem
Xavier Goaoc Université Paris-Est Marne-la-Vallée
19 janv. 2017
14h
15h30
23 févr. 2017
14h
15h30
23 mars 2017
14h
15h30
20 avr. 2017
14h
15h30
11 mai 2017
14h
15h30
22 juin 2017
14h
15h30

Le séminaire bénéficie du soutien de l'Institut Henri Poincaré.

Le comité scientifique est constitué de:

Le comité d'organisation est constitué d'Éric Colin de Verdière, Steve Oudot et Vincent Pilaud.