Research

Publications

  1. The linearized Calderón problem in transversally anisotropic geometries
    (with Slava Kurylev, Matti Lassas, Tony Liimatainen and Mikko Salo)
    preprint, arXiv 1712.04716, 27 pages, 2017.
  2. From semiclassical Strichartz estimates to uniform Lp resolvent estimates on compact manifolds
    (with Nicolas Burq and Katya Krupchyk)
    Int. Math. Res. Not. rnx042, 27 pages, 2017.
  3. Stability estimates for the Calderón problem with partial data
    (with Pedro Caro and Alberto Ruiz)
    J. Differential Equations, Vol. 260, No. 3, pp 2457 – 2489, 2016.
  4. The Calderón problem in transversally anisotropic geometries
    (with Slava Kurylev, Matti Lassas and Mikko Salo),
    J. Eur. Math. Soc., Vol. 18, No. 11 pp. 2579 – 2626, 2016.
  5. Stability estimates for the Radon transform with restricted data and applications
    (with Pedro Caro and Alberto Ruiz)
    Advances in Math., Vol. 267, pp 523 – 564, 37 pages, 2012.
  6. Stability estimates for an inverse scattering problem at high frequencies
    (with Habib Ammari, Hajer Bahouri and Isabelle Gallagher)
    J. Math. Anal. Appl., Vol. 400, No. 2, pp 525 – 540, 2013.
  7. On Lp resolvent estimates for Laplace-Beltrami operators on compact manifolds
    (with Carlos Kenig and Mikko Salo)
    Forum Math., Vol. 26, No. 3, 815 – 849, 2014.
  8. Global and local regularity of Fourier integral operators on weighted and unweighted spaces
    (with Wolfgang Staubach)
    Mem. Amer. Math. Soc., Vol. 229, No 1074, 2013.
  9. Determining an unbounded potential from Cauchy data in admissible geometries
    (with Carlos Kenig and Mikko Salo)
    Comm. Partial Differential Equations, Vol. 38, No. 1, pp 50 – 68, 2013.
  10. 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.
  11. 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.
  12. On the linearized local Calderón problem
    (with Carlos Kenig, Johannes Sjöstrand, Gunther Uhlmann)
    Math. Res. Letters, Vol. 16, No. 6, pp 955 – 970 , 2009.
  13. Limiting Carleman weights and anisotropic inverse problems
    (with Carlos Kenig, Mikko Salo, Gunther Uhlmann)
    Invent. Math., Vol. 178, No. 1, pp 119–171, 2009.
  14. 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.
  15. Sharp Lp Carleman estimates and unique continuation
    Duke Math. J., Vol. 129, No. 3, pp 503–550, 2005.
  16. Strichartz estimates for non-selfadjoint operators and applications
    Comm. Partial Differential Equations, Vol. 29, No. 1 & 2, pp 263–293, 2004.

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.

Recent conferences

  • Harmonic Analysis, PDEs and Geometry, ICMAT, Madrid, May 2013
  • Geometry and Inverse Problems, BIRS, Banff, September 2013
  • Workshop on Inverse Problems and Imaging, IHP, Paris, April 2014
  • PICOF, Hammamet, May 2014
  • Recent progress for Mathematical and Numerical analysis of Inverse Problems, CIRM, Marseille, May 2014
  • Three days in Analysis, Madrid, June 2014
  • The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, session on Inverse Problems, July 2014
  • Harmonic Analysis and Partial Differential Equations: Recent Developments and Future Directions, conference in honor of Carlos Kenig, Chicago, September 2014
  • Problèmes inverses et domaines associés, GOMS, Marseille, November 2014
  • Applied Inverse Problems, Helsinki, May 2015
  • Inverse problems workshop, Reims, June 2015
  • New Trends in Theoretical and Numerical Analysis of Waveguides, Porquerolles, May 2016
  • Dirichlet-to-Neumann Maps: Spectral Theory, Inverse Problems and Applications, CMO-BIRS, Oaxaca, May 2016
  • Control and Inverse Problems of Partial Differential Equations, Zhejiang University, Hangzhou, October 2016
  • Carleman estimates, unique continuation and applications, UCL, London, November 2016
  • Eighth Itinerant Meeting in PDEs, BCAM, Bilbao, January 2017
  • Third Symposium on Spectral and Scattering Theory, Florianopolis, July 2017
  • Mathematical Methods of Inverse Scattering and Spectral Theory, University of Leeds, September 2017
  • Contrôle et dynamique des EDP, Nancy, March 2018
  • Problèmes spectraux en physique mathématique, Dijon, May 2018

Recent talks

  • Journée Problèmes Inverses, Université de Cergy-Pontoise, February 2013
  • Institut Élie Cartan, September 2013
  • Premier séminaire franco-tunisien d'EDP, Tunis, September 2013
  • Calderon-Zygmund seminar, University of Chicago, January 2014
  • Université Paris 13, May 2014
  • Marseille, November 2014
  • University of the Basque Country, Bilbao, February 2015
  • Université Paris 13, November 2015
  • Université de Bordeaux, December 2015
  • Université de Créteil - Paris Est, December 2016
  • Université de Nantes, May 2017