Coordinateur
Monsieur Jacques FÉJOZ 

Membres du jury

Monsieur Jacques FÉJOZ, Professeur des universités, Université Paris Dauphine - PSL, Coordinateur/ Rapporteur
Monsieur Marco MAZZUCCHELLI, Directeur de recherche CNRS, Institut de mathématiques de Jussieu – Paris Rive Gauche, Rapporteur
Monsieur Vadim KALOSHIN, Professeur, Inst. of Science and Techn. Austria (Ista), Rapporteur
Madame Marie-Claude ARNAUD, Professeure des universités, Institut de mathématiques de Jussieu – Paris Rive Gauche, Membre du jury
Monsieur Patrick BERNARD, Professeur des universités, Université Paris Dauphine - PSL, Membre du jury
Madame Eva MIRANDA, Professeure, Universitat Politècnica de Catalunya, Membre du jury
Monsieur Sylvain CROVISIER, Directeur de recherche CNRS, Université Paris Saclay, Membre du jury
Madame Tere M-SEARA, Professeure, Universitat Politècnica de Catalunya, Membre du jury

Abstract
We investigate a conventional tight-binding model for graphene. In this model, distortion of the honeycomb lattice is allowed, but penalized by a quadratic energy. We prove that the optimal 3-periodic lattice configuration has Kekulé O-type symmetry, and that for a sufficiently small elasticity parameter, the minimizer is not translation-invariant. Conversely, we prove that for a large elasticity parameter the translation-invariant configuration is the unique minimizer.

Abstract
The classical Yamabe problem seeks for a metric conformal to a given metric with constant scalar curvature. By rewriting the conformal factor in a suitable way, it is equivalent to minimizing the L² norm of the gradient under a constraint on the L^{2^*} - norm. This talk concerns an analogous variational problem for manifolds with boundary introduced by Escobar, which seeks for metrics with zero scalar curvature in the interior and constant mean curvature on the boundary. The variational formulation for functions is very similar, but the constraint is now on the boundary values of the function. I will introduce the problem and show how a compactness argument of Engelstein-Neumayer-Spolaor can be adapted to give quantitative stability for minimizers of this problem.

Abstract
In this talk, I will present the approach of stochastic quantization from Parisi and Wu in order to construct measures from Quantum Field Theory using parabolic dynamic. Following the Metropolis-Hastings algorithm, one considers a stochastic heat equation associated to the QFT as an infinite dimensional Langevin SDE and study its properties using tools from stochastic analysis and PDEs. After an introduction on the usual \Phi_d^4 model on the torus, I'll explain how this can be adapted to a random singular environment given by a continuous Anderson operator where we obtain exponential ergodicity. Joint work with Hugo Eulry.

Abstract
Food security is commonly monitored through household surveys, which are costly and vary in temporal frequency and spatial resolution. These surveys are increasingly difficult to implement, often disrupted or unable to achieve full geographic coverage. To address this, organizations are exploring machine learning approaches that combine survey data with auxiliary sources to estimate key indicators such as food consumption scores. We show how currently operational frequentist methods fall short in quantifying the uncertainty of these sensitive measurements, whereas the Bayesian paradigm offers a more robust and reliable framework in estimating food security conditions.