Olivier GRAF

PhD student (fourth-year) at Laboratoire Jacques-Louis Lions.
I am working under the supervision of Jérémie Szeftel.


firstname.lastname at upmc.fr
Office 15-16-301
Laboratoire Jacques-Louis Lions
Sorbonne Université
4, place Jussieu, 75252 Paris Cedex 05

A short CV can be found here

Research Interests

I am interested in mathematical general relativity with particular emphasis at low-regularity solutions of the Einstein equations. My work is in connection with the bounded L2 curvature theorem and uses the techniques developped around this result : nonlinear evolution and elliptic PDEs at low regularity, geometry of spacelike and null hypersurfaces, the framework of the proof of the nonlinear stability of Minkowski by Christodoulou-Klainerman. I am also interested in trapped surface formation mechanism.

Publications and Preprints

Seminar Talks

  • The spacelike-characteristic bounded L2 curvature theorem:
    • 10th Central European Relativity Seminar, Potsdam-Golm, February 2020
    • Séminaire Laurent Schwartz de l'Ecole polytechnique, November 2019
    • Seminar on mathematical general relativity, Laboratoire Jacques-Louis Lions, May 2019

Other Talks

  • Reading group on the article "Causal geometry of Einstein-vacuum spacetimes with finite curvature flux" (by Sergiu Klainerman and Igor Rodnianski) (October 2019, General relativity reading group, LJLL)
  • "Low regularity characteristic Cauchy problem in general relativity" (June 2019, PhD seminar, LJLL)
  • "Bootstrap techniques for nonlinear equations" (October 2018, PhD mini-courses, LJLL)
  • Reading group on the article "Characterisation of the energy of gaussian beams on lorentzian manifolds - with applications to black holes spacetimes" by Jan Sbierski (here is a link) (October 2018, General relativity reading group, LJLL)
  • Reading group on the article "A global analysis proof of the stability of Minkowski and the polyhomogeneity of the metric" by Peter Hintz and András Vasy (here is a link) (January 2018, General relativity reading group)
  • "Spherical harmonics, weighted Sobolev spaces and Poisson's problem" (November 2017, PhD mini-courses, LJLL)
  • "Well-posedness results for nonlinear wave equations in low regularity" (March 2017, PhD seminar, LJLL)
  • "Some shocks and explosions phenomena in semilinear and quasilinear wave equations" (February 2017, PhD mini-courses, ENS)
  • "Physical motivations for the Einstein Equations" (November 2015, PhD mini-courses, ENS)

General relativity reading group

Here is the web page of the reading group in general relativity that Cécile Huneau and I organise.

Groupe de travail des thésard.e.s en analyse des EDPs

I was the organiser of a monthly two hours mini-course by/for PhD students in analysis of PDE topics at the Laboratoire Jacques-Louis Lions.
A more precise description and list of talks for the years 2017-2018 can be found here . The new organisers are Ludovic Godard-Cadillac and Fatima-Ezzahra Jabiri.


During my PhD I have been a teaching assistant at Sorbonne Université for the following courses

  • Sequences, series and improper integrals (Second year undergraduate)
  • Topology and differential calculus (Third year undergraduate)
  • Functional analysis (Third year undergraduate)
  • Linear Algebra (First year undergraduate)
Material can be found here .