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".

News:

  • I am glad to have been awarded the Frontier of Science Award 2025 for my paper The characteristic gluing problem for the Einstein vacuum equations. Linear and non-linear analysis with Aretakis and Rodnianski.

Research

Decentralized Finance:

I am interested in the development of novel mathematical tools to investigate, analyze and understand the dynamics on blockchains.
The central goal is to make DeFi a safe space for retail investors and provide objective methods to discuss and measure DeFi activity for regulators, governments, institutional investors, etc.

For interested students: I will hold a lecture Topics in Decentralized Finance in spring 2025 at the UL Math Department.

General Relativity:

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

General Relativity:

  1. (with Rodnianski) Obstruction-free gluing for the Einstein equations.
    arXiv:2210.09663.
  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).

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.