TBA

• Michel Bonnefont

On set-valued intertwining duality for diffusion processes

• Laurent Miclo

Markov intertwinning relations were first developed in the finite state space setting to provide a probabilistic approach to convergence to equilibrium. We will see how to adapt this method to diffusions on Riemannian manifolds, through stochastic extensions of mean curvature flows.

TBA

• Marjolaine Puel

On weighted Poincaré inequalities for multivariate Liouville and elliptical distributions - Application to Global Sensitivity Analysis

• David Heredia

In this work, we develop new weighted Poincaré inequalities for two clases of multivariate probability measures: multivariate Liouville and elliptical contoured distributions. The former are established via a radial-type decomposition involving the Dirichlet distribution, while the latter are obtained through their spherical counterparts. We further extend this type of results to measures with prescribed copulas. Finally, we apply these results to global sensitivity analysis and illustrate their practical use in a flood model case study.

TBA

• Ons Rameh

Sub-exponential tails in biased run and tumble equations with unbounded velocities

• Luca Ziviani

Run and tumble equations are widely used models for bacterial chemotaxis. In this talk, we present the long-time behavior of run and tumble equations with unbounded velocities. We show existence, uniqueness and quantitative convergence towards a steady state. In contrast to the bounded velocity case, the equilibrium has sub-exponential tails and we have sub-exponential rate of convergence to equilibrium. This produces additional technical challenges. We are able to successfully adapt both Harris' type and L²-hypocoercivity. This is joint work with Emeric Bouin and Josephine Evans.

TBA

• Jordan Serres

Régularité des équations elliptiques à poids monomiaux

• Francesco Pagliarin

Dans cet exposé je présenterai des théorèmes de régularité $C^{0,\alpha}$ et $C^{1,\alpha}$ pour solutions d'équations elliptiques, en forme de divergence, avec poids monomiaux. A cause de la dégéneration/singularité des poids (qui ne sont pas forcement dans la classe des poids Muckenhoupt $A_2$) la théorie classique ne s'applique pas. Grace à des théorèmes d'approximations et à des inegalités de Sobolev uniformes en $\epsilon$ on pourra quand même démontrer la régularité holderienne des solutions. C'est un travail fait en collaboration avec G. Cora, G. Fioravanti et S. Vita.

TBA

• Tom Maitre

Les variables sous-gaussiennes sont somme de trois gaussiennes, d'après A. Song

• Max Fathi

Dans cet exposé, je présenterai des résultats récents de Antoine Song sur une conjecture prédisant que les variables 1 sous-gaussiennes peuvent être réalisées comme sommes d'un nombre borné de variables gaussiennes standard, en toutes dimensions. Song démontre cette conjecture en dimension 1, et donne des nouvelles estimations sur le nombre de gaussiennes nécessaires en dimension supérieure. Je parlerai aussi des motivations de ce problème, issues de la géométrie des convexes.

TBA

• Andreas Malliaris

TBA

• Pierre Gervais

Low-temperature asymptotics of the Poincaré and the log-Sobolev constants for Łojasiewicz potentials

• Aziz Ben Nejma

In 2024, Chewi and Stromme showed that, in the low-temperature regime, the behavior of the relative entropy with respect to a Gibbs measure reflects that of the underlying potential when the latter has a unique minimizer. They conjectured that this link extends more generally to potentials having multiple minimizers. In this talk, we show that this is not the case. We explain that when there are multiple minimizers, the geometry of the set of minimizers plays a direct role in how the constants in functional inequalities behave at low temperature.

TBA

• Ivan Gentil

TBA

• Patrick Cattiaux

TBA

• Louis-Pierre Chaintron

TBA

• Paul Invernizzi

Active Brownian particles with mean-field interaction: singular interactions and multiple invariant measures

• Oscar de Wit

We introduce a mean-field McKean-Vlasov model for a collective of ants. The model sustains two non-trivial dynamical behaviours: aggregation and lane formation. We show the well-posedness and mean-field limit for the particle model with singular interactions via a compactness method. We also show the existence of multiple invariant measures via perturbative Fourier-style bifurcation analysis, reflecting the aggregation and lane formation behaviours (joint work with Matthias Rakotomalala). We conclude with some open problems pertaining to interacting active Brownian particle models.