Tous les événements à venir

I will present recent work on the derivation of an effective dynamics for the correlations associated to a semilinear Klein-Gordon system with random initial data. Due to the lack of invariances of this system, the effective dynamics is led by the trivial resonances and is not of kinetic type. I will motivate and present the model and the main result, and give some elements of the proof. This is a joint work with Anne-Sophie de Suzzoni (Evry) and Annalaura Stingo (X).

I will present recent work on the derivation of an effective dynamics for the correlations associated to a semilinear Klein-Gordon system with random initial data. Due to the lack of invariances of this system, the effective dynamics is led by the trivial resonances and is not of kinetic type. I will motivate and present the model and the main result, and give some elements of the proof. This is a joint work with Anne-Sophie de Suzzoni (Evry) and Annalaura Stingo (X).

L’ordre du jour sera le suivant :

1) Adoption du Compte-Rendu du conseil du 10 juin (vote)

2) Informations générales

3) Plan de Gestion des Emplois des enseignants-chercheurs 2026 (vote

4) Questions diverses

...

Bilevel optimization is a rather young but very active sub-field of mathematical optimization. The main reason is that bilevel optimization problems can serve as a powerful tool for modeling hierarchical decision-making processes, which arise in various real-world applications such as in critical infrastructure defense, transportation, or energy. However, the nested structure of bilevel problems makes them intrinsically hard to solve—even if all parameters of the problem are exactly known. Further challenges arise if problems under uncertainty are considered.

In this talk, we begin with a brief introduction to the key concepts of bilevel optimization, covering the structure, characteristics, and commonly used reformulations of these problems. We then explore how techniques from robust optimization can be used to tackle bilevel problems under uncertainty. In particular, we highlight that the sources of uncertainty in bilevel optimization are much richer compared to classic, i.e., single-level, problems since not only the problem data but also the (observation of the) decisions of the two players can be subject to uncertainty.

Finally, we discuss recent algorithmic advances for solving mixed-integer linear bilevel problems with a binary lower level and a Gamma-robust treatment of lower-level objective uncertainty. To solve these Gamma-robust bilevel problems, we present an exact and problem-tailored branch-and-cut approach as well as a heuristic framework. The latter relies on solving a linear number of deterministic bilevel problems so that no problem-specific tailoring is required.

We are interested in the numerical study of the one-dimensional blood flow model with discontinuous mechanical and geometrical properties and friction. We present the mathematical model together with its nondimensional form. The investigation of all its

stationary solutions will be the main point of this talk since they are not given in a explicit or implicit form so numerical techniques proposed in Gómez-Bueno et. al (2021) will be used. Following the numerical study done in Pimentel-García et. al (2023) we propose high-order fully well-balanced numerical methods that are able to preserve all the discrete stationary solutions. These schemes are given as a combination of the Generalized Hydrostatic Reconstruction and well-balanced reconstruction operators. Moreover these methods are able to deal with more than one discontinuous parameter. Some numerical tests are shown to prove its well-balanced and high-order properties, and its convergence to the exact solutions. We will also show results applied to

blood flow networks.

A définir

A définir

Pour appliquer les méthodes à noyaux, nous avons besoin de noyaux faciles à calculer et suffisamment riches. Comment peut-on concevoir de "bons" noyaux sur les espaces non-euclidiens, notamment sur les espaces symétriques qui sont très récurrents dans les applications ? Nous proposons un nouveau résultat, le "théorème Lp de Godement" comme outil principal pour répondre à cette question. Nous étudions en particulier le cas des espaces symétriques qui sont des "cônes" (cônes de matrices de covariance), où la réponse trouve une forme bien concrète, avec applications à l'appui. Finalement, si on ne peut pas trouver de noyaux définis positifs, que faire ? On montrera qu'il est possible de faire beaucoup de choses avec des noyaux qui sont différence de deux noyaux définis positifs : au lieu d'apprendre dans des RKHS, on peut apprendre dans des RKKS (reproducing Kernel Krein Space).

A définir