## 4 événements

• Séminaire de Probabilités

### Mardi 20 mars 09:45-10:45 - Martin Huesmann - University of Bonn

The matching problem : macroscopic and microscopic behaviour

Résumé : In this talk, we consider the matching problem between the Lebesgue
measure and n iid uniformly distributed point masses on the unit cube.
Whereas the order of the asymptotic $L^2$ transport cost are known since
the seminal work of Ajtai-Komlos-Tusnady, the microscopic behaviour of
the optimal couplings is less clear.
We explain how a slightly relaxed version of this problem converges to a
stationary coupling between the Lebesgue measure and the Poisson point
process on $\R^d$ provided $d\geq 3$. Then, we present a local transport
cost estimate on $\R^2$ which shows in a quantitative way that the
optimal couplings are close to the identity plus a shift. This allows us
to construct a locally optimal transport map from Lebesgue to Poisson on
$\R^2$ which is not stationary but which has (in a certain sense)
stationary increments.
Based on joint work with Theo Sturm, Michael Goldmann and Felix Otto

• Séminaire MIP

### Mardi 20 mars 11:00-12:00 - Victor Michel-Dansac - IMT - INSA

Second order Implicit-Explicit Total Variation Diminishing schemes for the Euler system in the low Mach regime

Résumé : In this work, we consider the development of implicit explicit total variation diminishing (TVD) methods (also termed SSP : strong stability preserving) for the compressible isentropic Euler system in the low Mach number regime. The scheme proposed is asymptotically stable with a CFL condition independent from the Mach number and it degenerates, in the low Mach number regime, to a consistent discretization of the incompressible system. Since it has been proved by Gottlieb, Tadmor and Shu in 2001 that implicit schemes of order higher than one cannot be TVD (SSP), we construct a new paradigm of implicit time integrators by coupling first order in time schemes with second order ones in the same spirit as highly accurate shock capturing TVD methods in space. For this particular class of schemes, the TVD property is first proved on a linear model advection equation and then extended to the isentropic Euler case. The result is a method which interpolates from the first to the second order both in space and time, which preserves the monotonicity of the solution, highly accurate for all choices of the Mach number and with a time step only restricted by the non stiff part of the system. One and two dimensional test cases showing that the method indeed possesses the claimed properties are also presented. This is a joint work with G. Dimarco (Ferrara), R. Loubère (Bordeaux) and M.-H. Vignal (Toulouse).

Lieu : Amphi L. Schwartz

• Séminaire de Géométrie et Topologie

### Mardi 20 mars 11:00-12:00 - Maÿlis Limouzineau

Cobordismes legendriens et fonctions génératrices

Résumé : En géométrie de contact, les fonctions génératrices sont un outil
très classique et efficace pour l’études des sous-variétés legendriennes. On
s’intéressera ici aux cobordismes legendriens entre noeuds legendriens dans
l’espace de contact standard, plus spécifiquement à ceux équipés de fonctions
génératrices. On verra en particulier comment construire un groupe de
concordance analogue à celui des noeuds toplogiques.

Lieu : Bât 1R2, salle Pellos (205)

• Séminaire de Statistique

### Mardi 20 mars 11:00-12:00 - Paula Gordaliza - IMT & Université de Valladolid

Obtaining fairness using optimal transport theory

Résumé : Currently, algorithms are being used to make decisions, both large and small, in almost all aspects of our lives. But how do we know if these algorithms are biased, involve ilegal discrimination or are unfair ? The study of Fairness is developed in a framework in which it is assumed that there exists a protected variable, whose use as an input of the algorithm may imply discrimination. In this talk, a review of the main definitions of fairness in Machine Learning is done to focus in two of them, which are based either in the outcome of the algorithm or in the error committed by it, across the different groups determined by the protected variable. When a procedure lacks of one of this two kinds of fairness, we will say that it has Disparate Impact (DI) and Disparate Mistreatment (DM), respectively. In this situations, our goal is to combat discrimination. This can be done by modifying either the classifiers or the data itself. Our work falls into the second category and changes the input data using optimal transport theory.