Stefan Czimek

Professor of Mathematics at Leipzig University.

firstname.lastname at

Office 332
Mathematisches Institut
Augustusplatz 10
04109 Leipzig, Deutschland

I did postdocs at the Fields Institute, the University of Toronto and
ICERM at Brown University. I defended my PhD at the LJLL (Paris 6)
under the supervision of Jérémie Szeftel.

I am a co-organizer of the General Relativity & PDE seminar, member of the Leipzig Center for Mathematical Physics, and scientific member of the International Max Planck Research School "Mathematics in the Sciences".


In my research I use tools from analysis, PDE theory and differential geometry to study fundamental problems of general relativity.
More specifically, I am interested in:

  • Construction and analysis of spacelike initial data for the Einstein equations.
  • Control of solutions to the null structure equations, with sharp estimates in low-regularity geometric function spaces.
  • Solving the Einstein equations in low-regularity (continuation results, blow-up criteria).
  • Gluing problems for characteristic and spacelike initial data.

Publications and preprints

  1. (with Rodnianski) Obstruction-free gluing for the Einstein equations.
  2. (with Aretakis and Rodnianski) Characteristic gluing to the Kerr family and application to spacelike gluing.
    Comm. Math. Phys. 403, 275-327 (2023).
  3. (with Aretakis and Rodnianski) The characteristic gluing problem for the Einstein vacuum equations. Linear and non-linear analysis.
    Ann. Henri Poincaré (2023)
  4. (with Aretakis and Rodnianski) The characteristic gluing problem for the Einstein equations and applications.
    Duke Math. J. (to appear); see also arXiv:2107.02441.
  5. (with Graf) The spacelike-characteristic Cauchy problem of general relativity in low regularity.
    Ann. PDE 8, 22 (2022).
  6. (with Graf) The canonical foliation on null hypersurfaces in low regularity.
    Ann. PDE 8, 23 (2022).
  7. The localised bounded $L^2$-curvature theorem.
    Comm. Math. Phys. 372, 71-90 (2019).
  8. Boundary harmonic coordinates on manifolds with boundary in low regularity.
    Comm. Math. Phys. 371, 1131-1177 (2019).
  9. An extension procedure for the constraint equations.
    Ann. PDE 4, 2 (2018).


  • The Cauchy problem in general relativity, Ph.D. thesis, UPMC (Paris 6), 2017, 259 pages.
  • On the static metric extension problem (here), Master’s thesis at ETH Zurich, 2014, 21 pages.

Selected recent talks in seminars

  • 10/2023 General Relativity seminar, Sorbonne University, Paris
  • 05/2023 Analysis seminar, ETH Zurich
  • 01/2023 General Relativity seminar, University of Vienna
  • 11/2022 Analysis seminar, Oxford University
  • 11/2022 London PDE Seminar, Imperial College London
  • 11/2022 Analysis seminar, University of Edinburgh
  • 03/2022 Analysis/probability seminar, Max-Planck-Institute Leipzig
  • 11/2021 Colloquium, Black Hole Initiative, Harvard University
  • 11/2021 Colloquium, Gravity Initiative, Princeton University
  • 10/2021 GR and Geometric Analysis seminar, Columbia University
  • 10/2021 ICERM seminar, Brown University
  • 06/2021 Analysis Seminar, Caltech

Selected recent talks at workshops, conferences, and schools

  • 08/2024 MFO Oberwolfach workshop Mathematical Aspects of General Relativity
  • 12/2023 ESI workshop Mathematical Relativity: Past, Present, Future upon the occasion of Yvonne Choquet-Bruhat's 100th birthday
  • 07/2023 5h mini-course On null gluing, Domoschool 2023, Domodossola, Italy (see here)
  • 03/2023 8h mini-course On characteristic gluing, Mathematical GR spring school, Tubingen
  • 02/2023 3h Ringvorlesung General Relativity, MPI MIS Leipzig
  • 03/2022 6h mini-course On characteristic gluing, Harvard University
  • 08/2021 Mathematical Aspects of GR, MFO, Oberwolfach

Online talks

  • 07/2023 Link Main conference of Thematic Programme Spectral Theory and Mathematical Relativity, ESI Vienna
  • 11/2021 Link Colloquium, Black Hole Initiative, Harvard University

Teaching ressources

  • PDE II
  • For interested students: See also here for the Leipzig General Relativity & Analysis of PDE seminar.