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 a given singular or bordism homology class, like for example finding a surface representative of minimal genus of a second homology class or determining the simplicial volume of manifolds.
Outside of mathematics I'm mostly interested in powerlifting and coding various stuff ranging from simple programms that help with my research, over trying to build a trading bot, to solving the coding puzzles from Project Euler.
The minimal genus problem for right angled Artin groups
with Rachael Boyd and Jean Pierre Mutanguha
Essentiality and simplicial volume of manifolds fibered over spheres
with Jens Reinhold
The Minimal Genus of Homology Classes in a Finite 2-Complex
with Mark Pedron
Preprint: arXiv:2002.08485, to appear in Algebraic & Geometric Topology
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
37073 Goettingen, Germany
E-Mail: thorben.kastenholz at mathematik.uni-goettingen.de