Research

Publications

  1. On Lp resolvent estimates for Laplace-Beltrami operators on compact manifolds
    (with Carlos Kenig and Mikko Salo)
    preprint, arXiv:1112.3216, 31 pages, to appear in Forum mathematicum, 2011.
  2. Global and local regularity of Fourier integral operators on weighted and unweighted spaces
    (with Wolfgang Staubach)
    preprint, arXiv:1104.0234, 78 pages, 2011.
  3. Determining an unbounded potential from Cauchy data in admissible geometries
    (with Carlos Kenig and Mikko Salo)
    preprint, arXiv:1104.0232, 26 pages, accepted for publication in Comm. Partial Differential Equations, 2011.
  4. Stability estimates for the anisotropic wave equation from the Dirichlet-to-Neumann map
    (with Mourad Bellassoued)
    Inverse Problems and Imaging, Vol. 5, No 4, pp 745 – 773, 2011.
  5. Stable determination of coefficients in the dynamical anisotropic Schrödinger equation from the Dirichlet-to-Neumann map
    (with Mourad Bellassoued)
    Inverse Problems, Vol. 26, No. 12, 125010, 2010.
  6. On the linearized local Calderón problem
    (with Carlos Kenig, Johannes Sjöstrand, Gunther Uhlmann)
    Math. Res. Letters, Vol. 16, No. 6, pp 955 – 970 , 2009.
  7. Limiting Carleman weights and anisotropic inverse problems
    (with Carlos Kenig, Mikko Salo, Gunther Uhlmann)
    Invent. Math., Vol. 178, No. 1, pp 119–171, 2009.
  8. Determining a magnetic Schrödinger operator from partial Cauchy data
    (with Carlos Kenig, Johannes Sjöstrand, Gunther Uhlmann)
    Comm. Math. Phys., Vol. 271, No. 2, pp 467–488, 2007.
  9. Sharp Lp Carleman estimates and unique continuation
    Duke Math. J., Vol. 129, No. 3, pp 503–550, 2005.
  10. Strichartz estimates for non-selfadjoint operators and applications
    Comm. Partial Differential Equations, Vol. 29, No. 1 & 2, pp 263–293, 2004.

PhD Thesis & Habilitation

  1. Carleman estimates and applications to unique continuation and inverse problems
    Habilitation Habilitation, Université Paris 13, 2011.
  2. Sharp Lp Carleman estimates and applications
    PhD thesis, Université de Rennes, 2002.

Proceedings

  1. Sharp Lp Carleman estimates and unique continuation
    proceedings of the conference Journées Équations aux Dérivées Partielles, Forges–les–Eaux, 2003.
  2. Anisotropic inverse problems and Carleman estimates
    Séminaire X-EDP, 2008.

Conferences and workshops

  • Journées Équation aux Dérivées Partielles, Forges–les–Eaux, June 2003
  • Workshop on harmonic analysis Young Researcher Days of the HARP Network, Orléans, June 2003
  • Nonlinear Waves and Dispersive Equations, MFO, Oberwolfach, October 2003
  • Inverse Problems and Applications, BIRS, Banff, August 2006
  • Équations dispersives non-linéaires, summer school, University of Nice, September 2006
  • Analyse microlocale et harmonique pour les problèmes inverses, CIRM, Luminy, March 2007
  • Conference on Applied Inverse Problems 2007, University of British Columbia, Vancouver, June 2007
  • Workshop Analyse des Équations aux Dérivées partielles, Saint Raphaël, October 2007
  • Inverse Problems: Recent Progress and New Challenges BIRS, Banff, November 2008
  • Contrôle et Problèmes Inverses pour les EDPs : Aspects Théoriques et Numériques, CIRM, Luminy, February 2009
  • Premier colloque Franco-Tunisien de Mathématiques, Djerba, March 2009
  • The Paris-London Analysis Seminar, December 2009
  • Dispersion, concentration and blow-up in Partial Differential Equations, initially scheduled in Rome, relocated in IHP, Paris, after the eruption of volcano Eyjafjallajökull
  • The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications, session on Inverse Problems, May 2010
  • Équations d'évolution non-linéaires dispersives, CIRM, Luminy, June 2010
  • Mini-course, Special Trimestre in Inverse Problems, UAM, Madrid, May 2011,
  • Semiclassical and multiscale aspects of wave propagation, Heraklion, Crete, May 2012

Recent talks

  • Calderón-Zygmund Analysis Seminar, University of Chicago, January 2009
  • Chevaleret, Universités Paris 6-7, May 2009
  • Séminaire Méthodes Mathématiques en Imagerie, IHP, November 2009
  • Journées Contrôle et Problèmes inverses, Université Versailles-Saint Quentin, November 2009
  • Université de Poitiers, February 2010
  • University Heriot-Watt, February 2010
  • Calderón-Zygmund Analysis Seminar, University of Chicago, October 2010
  • Seminar on Inverse Problems, MSRI, Berkeley, October 2010
  • Tsukuba University, November 2010
  • Université de Metz, February 2011
  • Université d'Evry, February 2011
  • Université et ÉNS de Lyon, February 2011
  • Université de Nantes, September 2011
  • Moscow State University, November 2011
  • Université Paris 13, December 2011
  • Université Joseph Fourier, Grenoble, February 2012
  • Université d'Orléans, March 2012
  • Université de Toulouse, March 2012