GPP- membres

random matrix theory, integrable systems Matrices aléatoires; Déterminants de Hankel, Toeplitz et Fredholm; Systèmes intégrables; Polynômes orthogonaux

Research interests: Exactly-solvable models in statistical mechanics, integrability and combinatorics.

Statistical field theory

The goal of my research is to contribute to the rigorous analysis of elliptic two-dimensional integrable models along their combinatorial line. Over the years, these statistical mechanics models have been shown to exhibit rich analytic and algebraic structures, as well as surprising links to combinatorics. Yet, to this day, many of their aspects remain either conjectural or plainly unexplored. I focus my study on the eight-vertex model and related systems such as the 8VSOS model and the XYZ spin chain, as well as their higher-spin generalisations. One of my central aims is to address conjectures and open questions about the ground state of the XYZ spin chain along its combinatorial line for various boundary conditions. I am also interested in obtaining exact finite-size expressions for some interesting physical quantities. Ultimately, the analysis of their scaling limits for large systems will lead me to establish links with quantum field theory models in the continuum.

Orthogonal and circular ensembles in Random Matrix Theory, Asymptotic analysis of Toeplitz determinants and applications to physics

My research is currently focused on spatial phase separation occurring in some statistical models. This phenomenon appears when boundary conditions induce macroscopic effects on the system, resulting in the formation of several regions with distinct behaviours. These regions are separated by interfaces generally referred to as "arctic curves".