Research
Publications
- A Borg-Levinson theorem for magnetic Schrödinger operators on a Riemannian manifold
(with Mourad Bellassoued, Mourad Choulli, Yavar Kian and Plamen Stefanov)
preprint, arXiv 1807.08857, 35 pages, 2018. - 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. - From semiclassical Strichartz estimates to uniform L^{p} resolvent estimates on compact manifolds
(with Nicolas Burq and Katya Krupchyk)
Int. Math. Res. Not. rnx042, 27 pages, 2017. - 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. - 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. - 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. - 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. - On L^{p} resolvent estimates for Laplace-Beltrami operators on compact manifolds
(with Carlos Kenig and Mikko Salo)
Forum Math., Vol. 26, No. 3, 815 – 849, 2014. - 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. - 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. - 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. - 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. - On the linearized local Calderón problem
(with Carlos Kenig, Johannes Sjöstrand, Gunther Uhlmann)
Math. Res. Letters, Vol. 16, No. 6, pp 955 – 970 , 2009. - Limiting Carleman weights and anisotropic inverse problems
(with Carlos Kenig, Mikko Salo, Gunther Uhlmann)
Invent. Math., Vol. 178, No. 1, pp 119–171, 2009.
- 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. - Sharp L^{p} Carleman estimates and unique continuation
Duke Math. J., Vol. 129, No. 3, pp 503–550, 2005. - Strichartz estimates for non-selfadjoint operators and applications
Comm. Partial Differential Equations, Vol. 29, No. 1 & 2, pp 263–293, 2004.
Proceedings
- Sharp L^{p} Carleman estimates and unique continuation
proceedings of the conference Journées Équations aux Dérivées Partielles, Forges–les–Eaux, 2003. - 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
- Inverse and Spectral Problems for (Non)-Local Operators, Max Planck Instit¨t, Leipzig, September 2018
- Analysis of PDEs: unique continuation, stabilization, control and dispersive properties, IHP, Paris, November 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
- Journé Analyse & Physique mathématique, Metz, October 2018