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Oana Pocovnicu

Chapman fellow (postdoctoral fellow)

Address :
Department of Mathematics
Imperial College London,
South Kensington Campus
London, SW7 2AZ, United Kingdom
E-mail : o.pocovnicu imperial.ac.uk

Research interests:

(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.
  • 2009 M.S. in Mathematics, Alexandru Ioan Cuza University, Iasi, Romania.
  • 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.
  • 2007 M.S. in Mathematics, Superior Normal School in Bucarest (SNSB), Romania.
    Master thesis: Harmonic Analysis. Applications. Thesis advisor: Prof. Catalin Lefter.
  • 2006 B.S. in Mathematics (with honors), Alexandru Ioan Cuza University, Iasi, Romania.


  • Papers:



    Talks:

  • Conference "Vortices and solitons for classical and quantum fluids", CIRM, Luminy, France, March 2012 (invited)
  • Seminaire de l'equipe Mathématiques pour l'Industrie et la Physique (MIP), Institut Mathematique de Toulouse, France, March 2012 (invited)
  • Analysis and PDEs Seminar, UCLA, USA, January 2012 (invited)
  • London Analysis and Probability Seminar, UK, December 2011
  • Analysis Seminar Princeton University, USA, December 2011
  • Analysis Seminar New York University, USA, December 2011
  • Nonlinear Analysis Seminar, Rutgers University, November 2011
  • Szegö equation and inverse spectral problems for Hankel operators, Mittag-Leffler Institute, Sweeden, November 2011
  • The Szegö equation and its perturbations (slides) , Analysis Seminar, Imperial College London, UK, October 2011
  • Journée de rentrée de l'équipe Analyse Numérique et EDP, Université Paris-Sud, Orsay, France, September 2011
  • The Szegö equation seen as the resonant dynamics of a non-linear wave equation (slides)
    Workshop HANDDY, "Equations Hamiltoniennes et Dispersives: Dynamique" , Ile de Berder, France, September 2011
  • 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