Abstract
My presentation will focus on functional data, that is, data taking the form of functions. In practice, such data are never observed continuously, but rather in a discretized and often noisy form. I will specifically examine the impact of this discretization on estimation in the scalar-on-function linear model. My approach first consists in reconstructing the curves from the discrete observations, and then estimating the model using a penalized regression method with model selection. I will present theoretical results, in particular oracle inequalities and convergence rates, which highlight the role of the number of observation points. Finally, an application to energy consumption data will illustrate these results.

Abstract
In the domain of statistical mechanics, mean-field methods represent a useful tool in order to study the evolution of systems made up by a very high number of interacting particles. In this talk we will use these techniques to analyse the evolution of quantum systems where the number of particles is sent to infinity. After a short introduction about the classical counterpart of this topic, we describe the behaviour of N-body quantum systems, understanding how the mean-field approximation leads to a new equation, called Hartree equation. Finally, we discuss the short time well-posedness properties of this object. 

Abstract
We will talk about the  construction and the profile of finite-time blow-up solutions to the semilinear heat equation on a compact Riemannian manifold. While most known singularity formation mechanisms rely on Euclidean concentration profiles, we develop a framework adapted to the geometric setting. In particular, we localizing the solution in local charts, and sum up information to gain control of the solution in all the manifold.  In addition, we prove a stability result under suitable perturbations of the initial data.

Résumé 

Les jeux stochastiques partiellement observables constituent un modèle fondamental pour analyser les interactions stratégiques entre des joueurs disposant d'une information incomplète. Dans le cadre à deux joueurs, nous nous intéressons à la valeur uniforme, c'est-à-dire le gain moyen limite que chaque joueur peut garantir pour des horizons suffisamment grands. De précédents travaux ont montré que cette valeur peut ne pas exister et que, même lorsqu'elle existe, aucun algorithme ne permet de la calculer ou de l'approximer. Pour contourner ce problème, nous introduisons la classe des jeux stochastiques aveugles ergodiques. Nous démontrons que la valeur uniforme existe, que son approximation est décidable, tandis que son calcul demeure indécidable. Nous considérons ensuite le cadre partiellement observable, dans lequel une extension directe de l'ergodicité ne suffit pas à garantir l'existence de la valeur uniforme. En imposant des conditions de Doeblin, nous prouvons que la valeur uniforme existe et que le problème d'approximation est décidable. Dans le cadre à un joueur, c'est-à-dire celui des processus de décision markoviens partiellement observables (POMDPs), nous étudions des objectifs de parité. Pour ces objectifs, les analyses limite-sûre et quantitatives sont généralement indécidables. Nous nous concentrons donc sur les POMDP révélateurs, où chaque état visité est annoncé avec une probabilité strictement positive. Nous montrons que l'analyse limite-sûre est EXPTIME-complète et que l'analyse quantitative peut être réalisée en EXPTIME. Dans le cadre multi-joueurs, nous définissons les notions de monitorabilité et de monitorabilité robuste. Nous observons que, si les chaînes de Markov aveugles sont monitorables, cette propriété disparaît dès qu'un joueur ou des signaux sont ajoutés. Cela nous amène à introduire une condition spécifique, l'atteignabilité approximativement bornée, sous laquelle la monitorabilité est retrouvée. Enfin, nous identifions des conditions suffisantes, l'ergodicité et la primitivité, qui impliquent l'atteignabilité approximativement bornée et garantissent la monitorabilité robuste.

Summary

Partially observable stochastic games provide a central model for studying strategic interaction between players under partial observation. We first investigate the uniform value, i.e., a limiting average payoff that both players can guarantee for sufficiently large horizons, in the two-player setting. Prior work showed that the uniform value may fail to exist and that, even when it does, no algorithm may compute or approximate it. We therefore introduce the class of ergodic blind stochastic games and prove that the uniform value exists, its approximation is decidable, while its computation remains undecidable. We then consider the hidden setting, where a direct extension of ergodicity is still insufficient to ensure existence. By considering Doeblin conditions, we prove that the uniform value exists and its approximation problem is decidable. Turning to the one-player setting of partially observable Markov decision processes (POMDPs), we study parity objectives, for which both limit-sure and quantitative analyses are undecidable in general. We consider revealing POMDPs, where each visited state is announced with positive probability. We establish that the limit-sure analysis is EXPTIME-complete and that the quantitative analysis can be achieved in EXPTIME. In the multi-player setting, we introduce the concepts of monitorability and robust monitorability. While blind Markov chains are shown monitorable, this property breaks when adding either a player or signals. This motivates the introduction of a structural condition, termed approximate bounded reachability, under which monitorability is recovered, although robustness may still fail. Finally, we show that classical mixing conditions, namely ergodicity and primitivity, imply approximate bounded reachability and guarantee robust monitorability.

Membres du jury

M. Guillaume VIGERAL, Professeur des universités, Université Paris 1 Panthéon-Sorbonne, Directeur de thèse
M. Eilon SOLAN, Professeur, Tel-Aviv University, Rapporteur
M. Stefan KIEFER, Professeur, Oxford University, Rapporteur
M. Bruno ZILIOTTO, Chargé de recherche, Toulouse School of Economics, Directeur de thèse
M. Pierre CARDALIAGUET, Professeur des universités, Université Paris Dauphine-PSL, Examinateur
M. Janos FLESCH, Associate professor, Maastricht University, Examinateur
Mme Patricia BOUYER-DECITRE, Directeur de recherche, Université Paris-Saclay, Examinatrice
M. Stéphane LEGENDRE, NyxAir, Invité

Abstract
The goal of this talk is to give a flavor of the kind of mathematics used in my field (exactly solvable models in statistical mechanics) and of the kind of question I am trying to address in my first project as PhD student. In the first part of the presentation, after saying a few words about near-critical models, I will introduce the spanning forests model and the dimer model. I will give the main definitions and theorems for the case of finite graphs and explain the relation between the two models know as Temperley's bijection. During the second part of the talk I will introduce the concept of partition probabilities for the spanning forests model and explain the explicit formulas that are known for these quantities. Lastly, if time allows I would like to say a few words about scaling limits results comparing what is known for the critical case and near-critical case.

Abstract
The ionic Euler–Poisson system serves as a hydrodynamic model for plasma, describing the motion of ions interacting with a background electron density. It is known that this three-dimensional system admits a family of one-dimensional solitary waves that propagate in a single direction with exponential localization. In this talk, we investigate the stability of these line solitary waves in the three-dimensional Euler–Poisson system. Since perturbations are allowed to depend on the transverse variables, this is referred to as transverse stability. We show that the line solitary waves are nonlinearly transversely stable: solutions starting close to a line solitary wave exist globally in time and converges in some suitable space to a modulated solitary wave as time tends to infinity.