Tony Lelièvre Room: Petit Amphi

Mickaël Latocca : Gibbs measure for NLS on the 2 sphere, part I

• Mickaël Latocca (Ecole Normale Supérieure (DMA), PSL Research University)

Room: Petit Amphi

Nicolas Camps : Gibbs measure for NLS on the 2 sphere, part II Room: Petit Amphi

Antoine Mouzard : Anderson $\Phi_2^4$ and stochastic quantization Room: Petit Amphi

Quentin Chauleur : Wave turbulence and Kolmogorov spectra Room: IBGBI building - Room A2 In this introductory talk I will sketch the derivation of the wave kinetic equation, with a particular emphasis on Kolmogorov-Zhakarov spectra wich appear as particular stationary states of the system. I will also show some classical results on energy transfer mechanisms in Hamiltonian nonlinear dispersive models, alongside numerical simulations.

Katja Vassilev : One-dimensional wave-kinetic theory Room: IBGBI building - Room A2 Abstract: Wave kinetic equations have been rigorously derived up to the kinetic timescale from dispersive systems in dimension $d \geq 2$. In this talk, we address the question of deriving kinetic equations in dimension one. Similar to higher dimensional models, one may expand the solution into iterates, represented by Feynman diagrams. However, the combinatorial estimates needed to bound these diagrams are much worse in dimension one, leading to some of these diagrams diverging at times much shorter than $T_{\mathrm{kin}}$. We explain this phenomena for the MMT (Majda, McLaughlin, and Tabak) model, a 1D model encompassing a range of dispersion relations, including the case of the 1D NLS. In this case, the kinetic equation is trivial, so we will discuss the question of what the appropriate kinetic theory could be in this setting.

Angeliki Menegaki : On the stability of Rayleigh--Jeans solutions for FPUT Room: IBGBI building - Room A2

Ricardo Grande : Extreme waves and large deviations for 2D pure gravity deep water waves Room: IBGBI building - Room A2 We study the formation of extreme waves from a statistical viewpoint in the context of the pure gravity water wave equations in deep water. We quantify their probability under random Gaussian sea initial data up to the optimal timescales allowed by deterministic well-posedness theory. The proof shows that rogue waves most likely arise through “dispersive focusing”, where phase synchronization produces constructive amplification of the water crest. The main difficulty in justifying this mechanism is propagating statistical information over such long timescales, which we overcome by combining normal forms and probabilistic methods. Unlike previous results, this novel approach does not require approximate solutions to be Gaussian. This is a joint work with M. Berti, A. Maspero and G. Staffilani.

Annalaura Stingo : Trivial resonances for a system of Klein-Gordon equations and applications in wave turbulence Room: IBGBI building - Room A2

Charles-Edouard Bréhier : Some structure-preserving schemes for SPDEs Room: IBGBI building - Room A2 I will present several topics on numerical methods for SPDEs, where standard schemes do not preserve important qualitative features of the solution. Precisely, I will show the construction and analysis of positivity, regularity and asymptotic preserving schemes for some SPDEs.

Arnaud Debussche : Stochastic primitive equations with transport noise and weak hydrostatic assumption Room: IBGBI building - Room A2 We investigate the convergence of solutions of a stochastic 3D Navier-Stokes equations to those of the primitive equations. We explore the impact of relaxing the hydrostatic assumption in the stochastic primitive equations by retaining martingale terms as deviations from hydrostatic equilibrium. This modified model, obtained through a specific asymptotic scaling accessible only within the stochastic framework, captures non-hydrostatic effects while remaining within the primitive equations formalism. We prove that it provides a higher-order approximation of the 3D stochastic Navier-Stokes equations.

El Mehdi Haress Room: IBGBI building - Room A2

Katharina Schratz : Resonances as a computational tool Room: IBGBI building - Room A2