About
Introduction.
I am a third year graduate student under the supervision of Nicolas Burq and Frédéric Rousset. I'm interested in the asymptotic dynamics of solutions to nonlinear dispersive PDE's, such as Schrödinger equations, with random initial data in supercritical regimes.
Keywords.
Nonlinear Schrödinger equation, Probabilistic Cauchy theory, Distroted Fourier transform, Asymptotic stability, Scattering, Semiclassical analysis, Imethod, Harmonic analysis, Schrödinger equation on compact manifolds.
Research Interests.
Schrödinger with a potential
In the presence of a shortrange potential, the nonlinear Schrödinger equation may have a centermanifold made of ground states solutions. Following the work of A. Soffer and M.I. Weinstein, one can prove asymptotic stability for small energy data of these coherent states. I investigated the asymptotic dynamics of a probabilistic flow below the energy space, and proved that asymptotic stability holds almostsurely.
Scattering below the energy space
Over the last decades, modified energy strategies and the socalled Imethod were widely used and refined in an effort to settle largetime dynamics questions for solutions to energysubcritical dispersive equtions. Folowing a series of works on the almost sure global wellposedness theory, I make use of the Imethod with a Morawetz bootstrap in a stochastic setting to prove alsmotsure scattering for a probabilistic flow in a supercritical regime, for an energysubcritical Schrödinger equation.
Schrödinger on the sphere
I am interested in the adaptation to the sphere of the pionner works of Bourgain on the torus, who investigated the Schrödinger equation on the support of the Gibbs measure thanks to the stochastic nonlinear smoothing gain for the Duhamel term. However, for NLS on the sphere, some bad interactions rule out any possible smoothing and new insights are needed.
Publications and Preprints
Publications
2020

Asymptotic stability of small ground states for NLS under random perturbations, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, to appear.
Preprints
2021

Scattering for the cubic Shrödinger equation in 3D with randomized initial data
Curriculum Vitae
Education
Ph.D
Laboratoire de Mathématiques d'Orsay
2019  Present
Dynamical behavior of dispersive PDE’s: from explicit solutions to generic dynamics
Under the supervision of Nicolas Burq & Frédéric Rousset
Magistère of Mathematics
ENS ParisSaclay & University ParisSaclay
2015  2019
 20182019: Master "AMS" in Mathematics, Orsay (with high honours),
 20172018: Agrégation de Mathématiques, (national french teaching competitive exam) Rank: 11th,
 Second concours de l’ENS (Ranks : 8th at ENS ParisSaclay, 7th at ENS Rennes),
 Bachelor in Mathematics, Orsay (with high honours, Laureate of Hadamard grant)
Classes préparatoires
2012  2015
 MPSI/MP*, Lycée Joffre (Montpellier)
Teaching Experience
Assistant at Laboratoire de Mathématiques d'Orsay
 Differential Calculus and Geometry, 20202021,Magistère 1st year,
 Differential Calculus and Topology, 20202022,Bachelor 3rd year,
 Linear Algebra,20202021,Bachelor 2nd year,
Assistant at IUT d’Orsay, Université Paris Saclay
 Calculus, 20192020, Bachelor 1st year.
Other
Responsibilities
July 2021
 Organization commitee of the Conference in honnor of Patrick Gerard's 60th anniversary , Orsay
20192021
 coorganizer of the seminar for gradute students in Analysis, Orsay
Semesters
September  December 2021
 Invited to the Semester "Hamiltonian technics in dispersive PDE's", ICERM
Conferences
Given talks
Seminars
 Séminaire des doctorants en EDP, Orsay, Octobre 2020
 Séminaire de vulgarisation des doctorants, Orsay, April 2021
 Séminaire de ANEDP, Orsay, June 2021
Conferences
 Conference on Schrödinger equation, Le Croisic, May 2021
Attended conferences and worshops
2021
 Colloque Analyse Harmonique et EDP, Evry, France, July .
 Conference in honnor of P. Gérard 60th anniversary, Orsay, France, July .
 Journées EDP, Obernai, France, June .
2020
January
 11th Itinerant Workshop in PDEs, Haussdorff Center for Mathematics, Bonn, Germany.
Contact
Location:
Université ParisSud, 91405, Orsay Cedex, France
Office:
Batiment 307, office 2A1.