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.
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".
Research
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
- (with Rodnianski) Obstruction-free gluing for the Einstein equations. arXiv:2210.09663.
- (with Aretakis and Rodnianski) Characteristic gluing to the Kerr family and application to spacelike gluing. Comm. Math. Phys. 403, 275-327 (2023).
- (with Aretakis and Rodnianski) The characteristic gluing problem for the Einstein vacuum equations. Linear and non-linear analysis. Ann. Henri Poincaré (2023)
- (with Aretakis and Rodnianski) The characteristic gluing problem for the Einstein equations and applications. Duke Math. J. (to appear); see also arXiv:2107.02441.
- (with Graf) The spacelike-characteristic Cauchy problem of general relativity in low regularity. Ann. PDE 8, 22 (2022).
- (with Graf) The canonical foliation on null hypersurfaces in low regularity. Ann. PDE 8, 23 (2022).
- The localised bounded $L^2$-curvature theorem. Comm. Math. Phys. 372, 71-90 (2019).
- Boundary harmonic coordinates on manifolds with boundary in low regularity. Comm. Math. Phys. 371, 1131-1177 (2019).
- An extension procedure for the constraint equations. Ann. PDE 4, 2 (2018).
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 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