Stefan Behrens

Bielefeld University
Faculty of Mathematics
Universitätsstraße 25
33615 Bielefeld

Office V3-232

About me

I am a mathematician at Bielefeld University working in the Geometry and Topology group. My field of research is low dimensional topology with a focus on the topology of smooth 4-manifolds. I received my PhD in 2014 from the University of Bonn under the supervision of Peter Teichner at the Max Planck Institute for Mathematics. Before coming to Bielefeld I held postdoc positions at the Alfréd Rényi Institute of Mathematics in Budapest (with András Stipsicz) and at Utrecht University (with Marius Crainic).

Research Interests

I am interested Heegaard-Floer and Seiberg-Witten theory and their application to 4-manifold theory. Recently, I have been thinking about various incarnations of so called correction terms (or d-invariants or Froshov invariants) and what they have to say about intersection forms of 4-manifolds with non-empty boundary. I also have a continued interest in what I like to call "surface valued Morse theory". By this I mean the study certain types of maps from 4-manifolds to surfaces (mostly the 2-sphere) and resulting combinatorial descriptions of 4-manifolds in terms of curve configurations of surfaces.

Here's a list of my mathematical interests:

  • The topology of 4-Manifolds (mainly smooth but also topological)
  • Heegaard-Floer and Seiberg-Witten theory (both theory and applications)
  • Stable homotopy theory (with a view toward applications to Seiberg-Witten theory)
  • (Broken) Lefschetz fibrations and related creatures (wrinkled fibrations, Morse 2-functions, ...)


Heegaard Floer correction terms, with a twist (with M. Golla)
to appear in Quantum Topology
Elimination of cusps in dimension 4 and its applications (with K. Hayano)
Proc. Lond. Math. Soc., Vol. 113 (2016), No. 5, 674-724
On 4-Manifolds, Folds and Cusps
Pacific J. Math., Vol. 264 (2013), No. 2, 257-306

(Lecture) Notes

Conferences, Workshops, etc.

Here's a selection of some my conference highlights and a (most likely outdated) list of future events. Just in case anyone is wondering where they might have met me, or appreciates a warning where they might run into me in the near future.

Where I will be:

Where I was:


In the winter semester 2017/2018 I am organizing the exercise classes for Analysis I.

Previous teaching:

Last update: October 9, 2017