Stefan Czimek

Professor of Mathematics at Leipzig University.

firstname.lastname at uni-leipzig.de

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.

News

  • I am a co-organizer of the upcoming workshop Women in Mathematical Relativity on 14. April 2023 (workshop homepage and poster). Female students in Bachelor's and Master's programs are especially encouraged to participate.
  • I am a co-organizer of the Leipzig General Relativity seminar.
  • I will hold (together with Dejan Gajic) a Ringvorlesung about general relativity at the MPI Leipzig in February 2023.
  • I will hold a mini-course about null gluing at this spring school in February-March 2023 (see poster).


Research

In my research I use tools from analysis, PDE theory and differential geometry to study fundamental problems of general relativity.
More specifically, I have been working on the following topics:

  • 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.


Research group

There are opportunities to join my research group by writing a Bachelor's and Master's thesis, or come in as Ph.D. student or post-doc. For the latter two, the International Max Planck Research School (IMPRS) can be found here.


Publications and preprints

  1. (with Rodnianski) Obstruction-free gluing for the Einstein equations. arXiv:2210.09663, 81 pages.
  2. (with Aretakis and Rodnianski) Characteristic gluing to the Kerr family and application to spacelike gluing. arXiv:2107.02456, 88 pages.
  3. (with Aretakis and Rodnianski) The characteristic gluing problem for the Einstein vacuum equations. Linear and non-linear analysis. arXiv:2107.02449, 102 pages.
  4. (with Aretakis and Rodnianski) The characteristic gluing problem for the Einstein equations and applications. arXiv:2107.02441, 31 pages.
  5. (with O. Graf) The spacelike-characteristic Cauchy problem of general relativity in low regularity. arXiv:1909.07355, 91 pages; accepted in Ann. PDE.
  6. (with O. Graf) The canonical foliation on null hypersurfaces in low regularity. arXiv:1909.07345, 69 pages; accepted in Ann. PDE.
  7. The localised bounded $L^2$-curvature theorem. Comm. Math. Phys. (2019), 20 pages.
  8. Boundary harmonic coordinates on manifolds with boundary in low regularity. Comm. Math. Phys. (2019), 47 pages.
  9. An extension procedure for the constraint equations. Ann. PDE (2018), 4:2, 122 pages.

Theses

  • 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 conferences and seminars

  • American Mathematical Society
  • Black Hole Initiative @ Harvard University
  • Brown University
  • Caltech
  • Canadian Mathematical Society
  • Columbia University
  • Fairbanks, Alaska
  • Fields Institute
  • Freiburg University
  • Gravity Initiative @ Princeton University
  • Imperial College London (2 hours)
  • Institut Fourier @ Grenoble
  • Laboratoire de Mathématiques et Physique Théorique @ Tours
  • Leipzig University
  • MFO, Oberwolfach
  • Oxford University
  • Paris 6 (Université Pierre-et-Marie-Curie)
  • UC Irvine
  • UConn
  • University of Edinburgh
  • University of Konstanz
  • University of Miami
  • University of Toronto
  • University of Vienna
  • Vanderbilt University