MokaMeetings

Team seminars are called MokaMeetings. They are organized on a monthly basis. Subscribe to the mailing list to be notified about upcoming seminars.

The list of past seminars is available here.

  • Mokameeting du 8 juin 2022 : Alex Delalande

    Un Mokameeting aura lieu le mercredi 8 juin 2022, à 14h, dans la salle P. Flajolet. Nous aurons le plaisir d’écouter Alex Delalande (Orsay)

    Titre : Quantitative stability of barycenters in the Wasserstein space

    Résumé : Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields such as image/geometry/language processing, which calls for the study of their statistical properties. A natural question in this spirit is the question of the stability of Wasserstein barycenters: given a set of probability measures, how does a perturbation of these measures affect the corresponding barycenters?
    In this talk, I will present a recent joint work with Guillaume Carlier and Quentin Mérigot where we tried to answer this question. We show that the Wasserstein barycenter depends in a Hölder-continuous way on the data, under relatively mild assumptions. Our proof relies on recent quantitative stability estimates for optimal transport maps and a new result quantifying the modulus of continuity of the push-forward operation under a (not necessarily smooth) optimal transport map.

  • Mokameeting du 16 mars 2022 : Matt Jacobs

    Un Mokameeting aura lieu le mercredi 16 mars 2022, à 16h. Il aura lieu en mode hybride : sur Discord ou dans la salle JLL1.
    Nous aurons le plaisir d’écouter Matt Jacobs (Purdue University)

    Titre : Extending the JKO scheme beyond Wasserstein-2 gradient flows

    Résumé : Since the pioneering work of Jordan, Kinderlehrer, and Otto (JKO), optimal transport has been a powerful tool to study PDEs that can be viewed as gradient flows with respect to the Wasserstein-2 metric.  In particular, the optimal transport perspective can be used to create a variational discrete-in-time approximation scheme (the JKO scheme).  The JKO scheme has many favorable properties that make it attractive for both theory and numerical simulation.

    In this talk, I will discuss extensions of the JKO scheme to more general PDEs that cannot be viewed as Wasserstein-2 gradient flows, but can still be evolved using the Wasserstein-2 metric.  This includes PDEs featuring mass change such as the Stefan problem and certain tumor growth models, as well as parabolic-hyperbolic equations including the Navier-Stokes equations. This talk is based on joint works with Inwon Kim, Wilfrid Gangbo, Jiajun Tong, and Jaime Marian.