I am an assistant professor at IRMAR (University of Rennes).
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 nonlinear media.
I am particularly interested in the long-time dynamics of solutions to these equations, in singular regimes and in various analytical or geometric frameworks. A key aspect of this study is the Hamiltonian structure, which plays a fundamental role in understanding these dynamics. For an introduction to these topics, you may refer to these slides.
My thesis, Probabilistic approaches for nonlinear Schrödinger equations , was supervised by Nicolas Burq and Frédéric Rousset, and was defended at Orsay on September 2022. Here is a short introduction in french.
Research directions
- Long time dynamics of dispersive PDEs
- Influence of the background geometry on nonlinear waves
- Statistical description of nonlinear waves
- Hamiltonian system and Birkhoff normal forms