Speakers

Ground state properties of interacting bosonic systems

The interacting Bose gas is a system composed of a very large number of quantum particles with totally symmetric wavefunction. Below a critical temperature, a phase transition to a Bose-Einstein condensate is expected to occur, and collective behavior emerges from the underlying many-body theory.

At zero temperature we have precise information on the ground state energy and the low-lying spectrum of excitations (at least in certain scaling limits). However, much less is known close to the transition temperature. In this talk I will discuss how the free energy in the thermodynamic limit can be obtained through a suitable description of correlations. This is a joint work with Giulia Basti, Serena Cenatiempo, Andreas Deuchert.

A statistical analogue of soliton resolution for the focusing Schrödinger equation

We study the infinite-volume limit of Gibbs measures for the one-dimensional focusing, mass-subcritical nonlinear Schrödinger equation. Under the critical scaling, we show that the measure concentrates around a single soliton over a Gaussian background.

This program was initiated by Lebowitz-Rose-Speer (1988), who introduced the grand-canonical ensemble for the focusing NLS and conjectured the existence of a phase transition in the infinite-volume limit. This conjecture was partially confirmed in recent work by Tolomeo-Weber (2026). Building on a soliton-Gaussian decomposition, we complete the analysis of the critical regime and show that, in this case, the measure exhibits a soliton resolution.

The talk is based on joint work with Justin Forlano (Monash University) and Leonardo Tolomeo (University of Edinburgh).

Global well-posedness for the two-dimensional dispersive Anderson model and its large torus limit

In this talk, we consider the two-dimensional nonlinear Schrödinger equation with a multiplicative spatial white noise and a polynomial nonlinearity, also known as the dispersive Anderson model (DAM). The talk is divided into two parts.

In the first part, we study global well-posedness for the DAM on the plane. We proceed by using a gauge transform introduced by Hairer and Labbé (2015) on the parabolic Anderson model and constructing the solution as a limit of solutions to a family of approximating equations. To establish global well-posedness, we establish a priori bounds using the Hamiltonian structure of the equation and also Strichartz estimates. In order to control the logarithmic growth of the noise, we incorporate function spaces with polynomial weights in our analysis. This part is based on a joint work with Arnaud Debussche (ENS Rennes), Nikolay Tzvetkov (ENS Lyon), and Nicola Visciglia (University of Pisa).

In the second part, we show that the global solution of the DAM on the plane can be realized as a limit of the periodic global dynamics of the DAM as the period goes to infinity, given suitable initial conditions and periodization of the noise. Global well-posedness of the periodic DAM was shown by Tzvetkov and Visciglia (2023), but the global solutions are not uniform in periods due to the logarithmic growth of the noise. To overcome this issue, we introduce periodic weights and construct weighted function spaces on periodic domains, which allow us to obtain a priori bounds for solutions independent of the periodicity. This part is based on a joint work with Nikolay Tzvetkov (ENS Lyon).

The FBSDE for sine-Gordon in higher regions 

I will present a construction of the Euclidean sine–Gordon quantum field theory using probabilistic methods. The approach formulates the model through a stochastic control problem and a weak forward–backward stochastic differential equation (FBSDE).

The starting point is a detailed study of the perturbation theory associated with the sine–Gordon potential across the full subcritical regime. 

For a portion of the subcritical regime extending beyond the previous threshold, the construction can be made rigorous beyond perturbation theory using the weak FBSDE and the associated stochastic control problem.

I will explain the different regimes of the model and give an idea of what is missing for a construction in the full subcritical regime. 

Gibbs measures and KMS states for the focusing nonlinear Schrödinger equation

The KMS (Kubo-Martin-Schwinger) condition is a criterion from quantum mechanics that is used to classify the equilibrium states of an infinite dimensional quantum system. In this talk, we will introduce its classical counterpart, which classifies the equilibrium measures of the Liouville equation. In the defocusing case, it can be shown that the Gibbs measure is the unique KMS state for the nonlinear Schrödinger equation. In the focusing case, one introduces a local KMS state, which corresponds to the cut-off in the (renormalised) mass required when defining the Gibbs measure. We show that the cut-off Gibbs measure corresponds to a suitably localised KMS state. The proofs are based on techniques from Malliavin calculus and Gaussian integration by parts.

This is based on joint work Zied Ammari and Vedran Sohinger.

Unconditional well-posedness of the stochastic Korteweg-de Vries equation on the real line and on torus

We study well-posedness issues of the stochastic Korteweg-de Vries equation (SKdV) with an additive noise. By adapting an argument by Zhou (1997) to the stochastic setting, we prove optimal pathwise unconditional uniqueness for SKdV in L²(ℝ). As a far as concern the torus case, we obtain an analogous result by adapting the so-called normal form approach to the stochastic framework.