I am a post-doctoral researcher at Nantes (Laboratoire de Mathématiques Jean Leray)
My thesis Probabilistic approaches for nonlinear Schrödinger equations was supervised by Nicolas Burq and Frédéric Rousset, and was defended at Orsay on September 2022.
My research lies at the intersection of various approaches to the mathematical analysis of nonlinear dispersive partial differential equations, particularly Schrödinger equations. The latter appear in numerous physical models to describe the propagation of the envelope of a rapidly oscillating wave packet in weakly nonlinear media.
I am particularly interested in the long-time dynamics of solutions to these equations, in regimes that can be singular and within various analytical or geometric contexts. The Hamiltonian structure of the equations plays a key role in understanding these dynamics.
Research directions
- Long time dynamics of dispersive PDEs
- Cauchy problem for weakly dispersive PDEs
- Influence of the background geometry on nonlinear waves
- Statistical description of nonlinear waves
- Hamiltonian system and Birkhoff normal forms
These research directions involve a broad spectrum of mathematical tools and approaches, drawing from fields such as PDE analysis, Hamiltonian dynamical systems, space-time resonances, high-frequency limits, symplectic geometry, harmonic and stochastic analysis, as well as considerations in number theory, random matrices, and combinatorics.