Thorben Kastenholz

I'm a postdoc in mathematics at the Karlsruhe Institut of Technology. Before that I was a postdoc in Göttingen working under Thomas Schick. Even earlier, I was a PhD student at the University of Bonn supervised by Ursula Hamenstädt.

I'm mainly interested in geometric and differential topology. To be more precise I'm interested in characteristic classes and understanding fiber bundles. Furthermore I'm interested in understanding the quantitative and geometric properties of singular and bordism homology, like for example finding a surface representative of minimal genus of a second homology class or determining the simplicial volume of manifolds. All of my recent research was focused on bounded cohomology, which is a very natural framework to get a better quantitative understanding of homology and cohomology classes.

Outside of mathematics I'm mostly interested in powerlifting and coding various stuff ranging from simple programs that help with my research, over trying to build a trading bot, to solving the coding puzzles from Project Euler.

Publications

• Non vanishing of the fourth bounded cohomology of free groups and codimension 2 subspaces
  Preprint: arXiv:2309.05024
• Simplicial bounded cohomology and stability
  with Robin Sroka
  Preprint: arXiv:2503.22511
• Symplectic Groups, Mapping Class Groups and the Stability of Bounded Cohomology
  Preprint: arXiv:2308.14171
• The minimal genus problem for right angled Artin groups
  with Rachael Boyd and Jean Pierre Mutanguha
  Published: Geom. Dedicata 217 (2023) 93
  Preprint: arXiv:2108.02914
• Essentiality and simplicial volume of manifolds fibered over spheres
  with Jens Reinhold
  Published: Journal of Topology, Volume 16, Issue 1
  Preprint: arXiv:2107.05892
• The Minimal Genus of Homology Classes in a Finite 2-Complex
  with Mark Pedron
  Published: Algebr. Geom. Topol. 22(3): 1375-1415 (2022)
  Preprint: arXiv:2002.08485
• Homological Stability for Spaces of Subsurfaces with Tangential Structure
  Preprint: arxiv:1812.06781,
  to appear in Quaterly Journal of Mathematics
• Exponential torsion growth for random 3-manifolds
  with Hyungryul Baik, David Bauer, Ilya Gekhtman, Ursula Hamenstädt, Sebastian Hensel, Bram Petri and Daniel Valenzuela
  Appeared in Int. Math. Res. Not. IMRN, 21: 6497 - 6534

Contact

Thorben Kastenholz
Karlsruher Institut of Technology
Englerstrasse 2
76128 Karlsruhe, Germany

Office: 1.036
E-Mail: kastenholz at kit.edu