I am a CNRS researcher at IRMAR (Rennes, France).
- 2018-2021: PhD under the supervision of Patrick Gérard at the Laboratoire de Mathématiques d'Orsay (LMO).
- 2021-2022: Institute postdoc at ICERM (Brown University)
- 2022-2023: postdoc at the University of Basel with Enno Lenzmann
I am interested in the long time behavior of solutions to dispersive nonlinear PDEs. I mainly focus on PDEs with wery weak dispersion (for instance, the Schrödinger equation on the Heisenberg group) and on integrable PDEs (for instance, the Benjamin-Ono equation on the torus). Here is a lay summary of the zero-disperion limit problem for the Benjamin-Ono equation on the torus.
Here is my
PhD manuscript entitled "Long-time behavior of solutions to nonlinear PDEs: orbital stability of traveling waves, dispersion, integrability, damping".
Schrödinger equation on the Heisenberg group
• On the orbital stability of a family of traveling waves for the cubic Schrödinger equation on the Heisenberg group, Bulletin de la SMF, 149-1, 15--54, 2021 (arXiv, journal)
• On the radially symmetric traveling waves for the Schrödinger equation on the Heisenberg group, Pure and Applied Analysis 2-4, 739--794, 2020 (arXiv, journal)
Cauchy problem in low regularity for Schrödinger-type equations
• Pathological set with loss of regularity for nonlinear Schrödinger equations,
with Rémi Carles, 2023 (arXiv)
Refined probabilistic local well-posedness for a cubic Schrödinger half-wave equation, with Nicolas Camps and Slim Ibrahim, 2022 (arXiv)
• Pathological set of initial data for scaling-supercritical nonlinear
Schrödinger equations, with Nicolas Camps, IMRN, 2022 (arXiv, journal)
• Probabilistic local well-posedness for the Schrödinger equation posed for the Grushin operator, with Mickaël Latocca, Journal of Functional Analysis, 283--3, 2022 (arXiv, journal)
Benjamin-Ono equation on the torus
• Lax eigenvalues in the zero-dispersion limit for the Benjamin-Ono
equation on the torus, to appear in SIAM Journal on Mathematical Analysis, 2023 (arXiv)
• Zero-dispersion limit for the Benjamin-Ono equation on the torus with single well initial data, Communications in Mathematical Physics, 2023 (arXiv, journal)
• Long time behavior of solutions for a damped Benjamin-Ono equation, Mathematische Zeitschrift, 300, 1939--2006, 2022 (arXiv, journal)
• The third order Benjamin-Ono equation on the torus: well-posedness, traveling waves and stability, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 38-3, 815--840, 2021 (arXiv, journal)
• Cubic Schrödinger half-wave equation and random initial data, with Nicolas Camps and Slim Ibrahim, Journées équations aux dérivées partielles, 2022 (pdf)
- 2022: class « Measure - and Integration theory » at the University of Basel
- 2018-2021: teaching assistant at the mathematics department of the ENS Paris (DMA), exercices sessions to the Master 1 course « Functional analysis ».
- 2015-2018: oral exercises sessions at CPGE, an intensive undergraduate maths and physics course
I am co-author, with Thomas Blomme, Quentin Guignard and Bernard Randé, of a book of solutions to exercises given to the ENS and École Polytechnique entrance exam (at Calvage et Mounet).