Thomas Alazard


Education
HDR - Dec 2011 Université Paris-Sud 11 : “ Effets non linéaires et dispersifs dans les équations des vagues et de Schrödinger”
PhD - Dec 2005 Université Bordeaux I : “Dynamique des gaz à faible nombre de Mach”, Advisor Guy Métivier
1999-2003 École Normale Supérieure, Lyon


Academic positions
Jan 2021 - Jun 2021 Chancellor Professor at UC Berkeley
Since oct 2016 Directeur de recherche CNRS, École Normale Supérieure Paris-Saclay
Since oct 2016 Senior Adjunct Professor, École Normale Supérieure Paris-Saclay
sep 2014 - sep 2016 Junior Adjunct Professor, École Normale Supérieure
oct 2010 - sep 2016 Chargé de recherches CNRS, École Normale Supérieure
sep 2006 - sep 2010 Chargé de recherches CNRS, Université Paris-Sud 11
sep 2003 - sep 2006 Moniteur, Université Bordeaux I


PhD students
sep 2018 - jun 2021 Ayman Said (then postdoc at Duke University)
sep 2016 - sep 2019 Hui Zhu (codirection with Nicolas Burq; now postdoc at University of Michigan-Ann Arbor)
sep 2014 - sep 2017 Thibault de Poyferré (Miller fellowship at UC Berkeley)


Research and main recent publications

My research deals with nonlinear partial differential equations and in particular, since 2008,

  • water-wave equations,
  • paradifferential calculus (see the articles [4,6,7] below) and semi-classical analysis (see [5]),
  • dispersive estimates: Morawetz, Strichartz and smoothing effect ([1,3,5]),
  • small divisors problem and the Nash-Moser theory ([3]),
  • normal forms method ([3,4,5]),
  • control theory ([2]).
  • Parabolic free boundary value problems [8,9].

  1. A Morawetz inequality for water waves (with Mihaela Ifrim and Daniel Tataru)
    Amer. J. Math, 144 (2022), no. 3, 607-699.

  2. Control for water waves (with Pietro Baldi and Daniel Han-Kwan)
    J. Eur. Math. Soc. 20 (2018) 657-745

  3. Gravity capillary standing water waves (with Pietro Baldi)
    Arch. Ration. Mech. Anal., 217 (2015), no 3, 741-830

  4. Sobolev estimates for two dimensional gravity water waves (with Jean-Marc Delort)
    Astérisque 374 (2015), viii+241 pages

  5. Global solutions and asymptotic behavior for two dimensional gravity water waves (with Jean-Marc Delort)
    Ann. Sci. Éc. Norm. Supér., 48, (2015), no. 5, 1149-1238

  6. On the Cauchy problem for gravity water waves (with Nicolas Burq and Claude Zuily)
    Invent. Math., 198 (2014), 71-163

  7. On the water waves equations with surface tension (with Nicolas Burq and Claude Zuily)
    Duke Math. J., 158 (2011), no. 3, 413-499

  8. Endpoint Sobolev theory for the Muskat equation (with Quoc-Hung Nguyen)
    Commun. Math. Phys. 397 (2023), no. 3, 1043-1102.

  9. Paralinearization of the Muskat equation and application to the Cauchy problem (with Omar Lazar)
    Arch. Ration. Mech. Anal. 237 (2020), no. 2, 545-583.