Stefan Behrens

Bielefeld University
Faculty of Mathematics
Universitätsstraße 25
33615 Bielefeld

Office V3-232

About me

I am an assistant professor (wissenschaftlicher Assistent) in the Geometry and Topology group led by Prof. Dr. Stefan Bauer. My field of research is low dimensional topology with a focus on the topology of smooth 4-manifolds. Before coming to Bielefeld, I had stops in Bonn, Budapest, and Utrecht.

Research Interests

I am interested Seiberg-Witten and Heegaard-Floer 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 Froyshov invariants) and what they have to say about intersection forms of 4-manifolds with non-empty boundary. I am currently thinking about various Froyshov-type invariants that arise in the context of Manolescu's Seiber-Witten-Floer homotopy types.

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, ...)


Classification of boundary Lefschetz fibrations over the disc (with G. R. Cavalcanti and R. L. Klaasse)
"Geometry and Physics: A Festschrift in Honour of Nigel Hitchin, Volume II", Oxford University Press 2018
Heegaard Floer correction terms, with a twist (with M. Golla)
Quantum Topol., Vol. 9 (2018), No. 1, 1-37
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 & Books edited


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Here's a selection of some my conference highlights and a (most likely outdated) list of future events.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.

Last update: August 24, 2020