(Dispersive) Nonlinear Partial Differential Equations with tools from harmonic analysis, completely integrable Hamiltonian systems, complex analysis, and spectral theory. In particular, I am interested in the study of solitons and their stability, long time behavior of solutions (global existence, scattering, soliton resolution, growth of high Sobolev norms, and long time approximation by resonant dynamics), inverse problems for Hankel operators.
The equations I studied so far are Szegö equation, nonlinear Schrödinger equation, nonlinear wave equation, and Gross-Pitaevskii equation.
Education:
2011 Ph.D. in Mathematics (très honorable), Université Paris-Sud 11, Orsay, France.
Ph.D. thesis: Study of a nonlinear, non-dispersive, completely integrable equation and of its perturbations.
Thesis advisor: Prof. Patrick
Gérard.
2008 M.S. in Mathematics, "Analyse, Arithmétique et Géométrie" Program, Université Paris-Sud 11.
Master thesis: The long time behaviour in the neighborhood of special solutions
for the Gross-Pitaevskii equation. Thesis advisor: Prof. Patrick Gérard.
Non Linear PDEs Seminar (NLPDE), Kyoto University, Japan, August 2011
Analysis and PDEs Seminar, UCLA, USA, July 2011
Explicit formula for the solution of the Szegö equation on the real line and applications (slides)
Conference "Nonlinear Dispersive PDEs and Related Topics", Institut Henri Poincaré (IHP), Paris, France, June 2011
Analysis Seminar, Princeton University, USA, February 2011
"Problèmes spectraux en physique mathématique" Seminar, Institut Henri Poincaré (IHP), Paris, France, December 2010
Workshop "Asymptotic regimes for nonlinear Schrödinger equations", CIRM, Luminy, France, September 2010
Dispersive PDE Seminar, University of Toronto, Canada, July 2010
Ph.D. Students' Seminar, Université Paris-Dauphine 9, France, February 2010
Ph.D. Students' Seminar, Université Paris-Sud 11, France, February 2010
Fields Analysis Working Group, Fields Institute, Toronto, Canada, January 2010
Teaching:
Fall 2011: Functional Analysis M3P7, M4P7, M5P7, Imperial College, London, UK
(link to the course website)
Spring 2011: Algebra for second year undergraduate students in the Mathematics and Informatics program, Université Paris-Sud, Orsay, France
Fall 2008, 2009, 2010: Calculus for first year undergraduate students in the Mathematics, Physics and Informatics program, Université Paris-Sud, Orsay, France
Fall 2008, 2009: Projet Professionnel ("Project for Professions") for first year undergraduate students, Université Paris-Sud, Orsay, France