Bjoern Bringmann — Princeton University
The goal of these lectures is to study the global well-posedness of singular SPDEs. As a warm-up, we first prove the global well-posedness of the $\Phi^4_2$-model. We then turn to the global well-posedness of the stochastic Abelian-Higgs model, which is a stochastic geometric evolution equation. In this context, we also discuss covariant monotonicity formulas and covariant stochastic objects.
Scott Armstrong — Sorbonne University and CNRS
Aurelien Deya — Université de Lorraine and CNRS
We will first present the physical motivations behind this model, then turn to the comparison with its "standard" counterpart, in which the harmonic oscillator (on $\mathbb{R}^3$) is replaced by the Laplacian on the torus. The results, from joint work with Reika Fukuizumi (Tokyo) and Laurent Thomann (Nancy), include the interpretation of the model in the renormalized sense, the global existence and uniqueness of a solution, the existence of an invariant measure, and finally its uniqueness in the weak nonlinearity regime.
Hugo Eulry — ENS Lyon
Invariant measures play a central role in understanding the long-time behavior of dynamical systems, as they describe their statistical equilibrium. Conversely, understanding the dynamics provides valuable information about the corresponding invariant measures. In this talk, we will focus on the dynamical approach to invariant measures. After presenting the general strategy for proving unique ergodicity in case of parabolic SPDEs, we will discuss how these methods can be adapted to a non-translation-invariant framework for dynamics driven by a random operator. We will then show that similar ideas can also be adapted for dispersive equations, such as the stochastic damped wave equation, even when crucial properties such as the strong Feller property fail. This is based on joint works with Antoine Mouzard and Nikolay Tzvetkov.
Yingtong Hou — Université de Lorraine
Elias Nohra — Sorbonne University
In this talk, I will present some recent contributions to the study of the 2D Yang--Mills measure, based on joint works with Nguyen Viet Dang (Strasbourg). I will present results concerning the construction of the 2D Yang–Mills measure as a random distributional connection on general surfaces, using a novel gauge: the Morse gauge. I will describe its appearance as a universal scaling limit of lattice gauge models, and its semiclassical (small-area) limit.
Nikolay Tzvetkov — ENS Lyon