I am a postdoctoral researcher at the Karlsruhe Institute of Technology in the working group of Manuel Krannich, specialising in the area of Algebraic Topology. Before that, I was a doctoral and postdoctoral researcher at the University of Bonn and the Max Planck Institute for Mathematics in Bonn, in the working group of Carl-Friedrich Bödigheimer.

• Homepage at the KIT
• CV
• ORCID record

My research interests lie in the area of Algebraic and Geometric Topology: more specifically, I am interested in configuration spaces and topological moduli spaces, topological operads and their algebras, factorisation homology, automorphisms of manifolds and manifold bundles, as well as cobordism categories.

Publications

1. F. Kranhold. ‘A stable splitting of factorisation homology of generalised surfaces’. arXiv:2310.07688.
2. C.-F. Bödigheimer, F. Boes, and F. Kranhold. ‘Computations in the unstable homology of moduli spaces of Riemann surfaces’. arXiv:2209.08148.
3. A. Bianchi, F. Kranhold, and J. Reinhold. ‘Parametrised moduli spaces of surfaces as infinite loop spaces’. Forum Math. Sigma 10, e39 (2022), arXiv:2105.05772.
4. F. Kranhold. ‘Configuration spaces of clusters as E_d-algebras’. To appear in Homotopy Homol. Appl., arXiv:2104.02729.
5. A. Bianchi and F. Kranhold. ‘Vertical configuration spaces and their homology’. Q. J. Math. 73 (4 2022), pp. 1279–1306, arXiv:2103.12137.

Theses

• Coloured topological operads and moduli spaces of surfaces with multiple boundary curves. Doctoral thesis, University of Bonn, 2022.
• Moduli spaces of Riemann surfaces and symmetric products: A combinatorial description of the Mumford–Miller–Morita classes. Master’s thesis, University of Bonn, 2018.

Selected talk material

Here you can find handwritten notes or recordings of some talks I have given in the last years, some of them at multiple occasions:

• Parametrised moduli spaces of surfaces as infinite loop spaces. Recording Purdue.
• Configuration spaces of clusters as E_d-algebras. Recording Copenhagen.
• Vertical configuration spaces and their homological stability.
• The homotopy type of the cobordism category.
• Homotopy coherent multiplications and loop spaces.
• An introduction to model categories.

Courses

• Kategorientheorie: Grundlagen. Lecture notes (German) for a course I gave at the CdE-WinterAkademie 2023/24. It was accompanied by a set of exercises.