Papers
General relativity

The Bounded L^{2}
Curvature Conjecture (with S. Klainerman and
I. Rodnianski)
Invent. Math. 202 (1), 91216, 2015.

Sharp Strichartz estimates for the wave
equation on a rough background
Annales Scientifiques de
l'Ecole Normale Supérieure 49 (6), 12791309, 2016.

Global regularity for the 2+1 dimensional
equivariant Einsteinwave map system (with L. Andersson and
N. Gudapati)
Ann. PDE 3 (2), Art. 13, 142 pp., 2017.

Parametrix for wave equations on a rough
background III: spacetime regularity of the phase
Astérisque 401, 321 pp., 2018.

Global Nonlinear Stability of
Schwarzschild Spacetime under Polarized Perturbations (with S. Klainerman)
Annals of Math Studies, 210. Princeton University Press, Princeton, NJ, 2020, xviii+856 pp.

Constructions of GCM spheres in perturbations of
Kerr (with S. Klainerman)
Ann. PDE 8 (2), Art. 17, 153 pp., 2022.

Effective results on uniformization and
intrinsic GCM spheres in perturbations of Kerr (with S. Klainerman)
Ann. PDE 8 (2), Art. 18, 89 pp., 2022.

Parametrix for wave equations on a rough background I: regularity of the phase at initial time
Submitted.

Parametrix for wave equations on a rough background II: construction and control at initial time
Submitted.

Parametrix for wave equations on a rough
background IV: control of the error term
Submitted.

Kerr stability for small angular momentum (with S. Klainerman)
Submitted.

Wave equations estimates and the nonlinear stability of slowly rotating Kerr black holes (with E. Giorgi and S. Klainerman)
Submitted.
Finite time singularity formation and asymptotic stability

Standing ring blow up solutions to the Ndimensional quintic nonlinear Schrödinger equation (with P. Raphaël)
Comm. Math. Phys. 290 (3), 973996, 2009.

Stable self similar blow up dynamics for slightly L^{2} supercritical NLS equations (with F. Merle and P. Raphaël)
Geom. Funct. Anal. 20 (4), 10281071, 2010.

Existence and uniqueness of minimal blow up solutions
to an inhomogeneous mass critical NLS (with P. Raphaël)
J. Amer. Math. Soc. 24, 471546, 2011.

The instability of BourgainWang solutions for the L^{2} critical NLS (with F. Merle and P. Raphaël)
Amer. J. Math. 135 (4), 9671017, 2013.

On collapsing ring blow up solutions to
the mass supercritical NLS (with F. Merle and P. Raphaël)
Duke Math. J. 163 (2), 369431, 2014.

Codimension one stability of the
catenoid under the vanishing mean curvature flow in Minkowski space
(with R. Donninger, J. Krieger and W. Wong)
Duke
Math. J. 165 (4), 723791, 2016.

On the stability of type I blow up for
the energy super critical heat equation (with C. Collot and
P. Raphaël)
Mem. Amer. Math. Soc. 260, no 1255, v+97 pp., 2019.

On strongly anisotropic type I
blow up (with F. Merle and P. Raphaël)
Int. Math. Res. Not., 541606, 2020.

On blow up for the energy super critical defocusing non linear Schröodinger equations (with F. Merle, P. Raphaël and I. Rodnianski)
Invent. Math., 227 (1), 247413, 2022.

On the implosion of a compressible fluid I: Smooth selfsimilar inviscid profiles (with F. Merle, P. Raphaël and I. Rodnianski)
Annals of Math., 196 (2), 567778, 2022.

On the implosion of a compressible fluid II: Singularity formation (with F. Merle, P. Raphaël and I. Rodnianski)
Annals of Math., 196 (2), 779889, 2022.
Derivation of the nonlinear Schrödinger equation
Domain decomposition methods
Longtime existence problems on compact manifolds
Absorbing boundary conditions

Absorbing boundary conditions for reaction diffusion equation.
IMA J. Appl. Math. 68 (2), 167184, 2003.

Design of absorbing boundary conditions for Schrödinger equations in R^{d}.
SIAM J. Numer. Anal. 42 (4), 15271551, 2004.

A nonlinear approach to absorbing boundary conditions for the semilinear wave equation.
Math. Comp.75, 565594, 2006.

Absorbing boundary conditions for nonlinear scalar partial differential equations
Comput. Methods Appl. Mech. Engrg. 195, 37603775, 2006.

Absorbing boundary conditions for nonlinear Schrödinger equations
Numerische Mathematik 104, 103127, 2006.

Towards accurate artificial boundary conditions for nonlinear PDEs through examples (with X. Antoine and C. Besse)
Cubo, 11 (4), 2948, 2009.
Propagation/ reflection of singularities, smoothing effect
I defended my Habilitation thesis on October 8th 2012 (Univerité Paris 13).
You can download my Habilitation thesis in .pdf.
Between October 2000 and April 2004, I have been doing a PhD on
"Pseudodifferential and paradifferential calculus for the study of
absorbing boundary conditions and qualitative properties of nonlinear
PDE's" at Univerité Paris 13 under the guidance of Laurence Halpern.
You can download my PhD thesis in .pdf.
Here is the proceeding of the talk I gave at ICM 2014 The resolution of the bounded
L^{2} curvature conjecture in general relativity.