Olivier GRAF

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

Contact

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

  • (with Stefan Czimek) "The spacelike-characteristic Cauchy problem of general relativity in low regularity" arXiv:1909.07355
  • (with Stefan Czimek) "The canonical foliation on null hypersurfaces in low regularity" arXiv:1909.07345


Seminar Talks

  • "The spacelike-characteristic Cauchy problem with L2 bounded curvature" (May 2019, Séminaire de relativité générale du Laboratoire Jacques-Louis Lions)


Groupe de travail Talks

  • Reading group on the article "Causal geometry of Einstein-vacuum spacetimes with finite curvature flux" (by Sergiu Klainerman and Igor Rodnianski) (October 2019, Groupe de lecture in General Relativity)
  • "Low regularity characteristic Cauchy problem in general relativity" (June 2019, GTT du LJLL)
  • "Bootstrap techniques for nonlinear equations" (October 2018, Groupe de travail des thésard.e.s en analyse des EDPs)
  • 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, Groupe de lecture in General Relativity)
  • 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, Groupe de lecture in General Relativity)
  • "Spherical harmonics, weighted Sobolev spaces and Poisson's problem" (November 2017, Groupe de travail des thésard.e.s en analyse des EDPs)
  • "Well-posedness results for nonlinear wave equations in low regularity" (March 2017, GTT du LJLL)
  • "Some shocks and explosions phenomena in semilinear and quasilinear wave equations" (February 2017, Groupe de travail des thésard.e.s en analyse des EDPs)
  • "Physical motivations for the Einstein Equations" (November 2015, Groupe de travail des thésard.e.s en analyse des EDPs)


Groupe de lecture en relativité générale

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


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

I was the organizer of a monthly two hours mini-course by/for PhD students in 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 organizer is Ludovic Godard-Cadillac.


Teaching

During my PhD I've 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 .