Florian Kranhold

My research interests lie in the area of Algebraic and Geometric Topology. More specifically, I am interested in configuration spaces and topological moduli spaces, operads and their algebras, factorisation homology, and bordism categories.

Publications

• Segal K-theory of vector spaces with an automorphism (arXiv), with Andrea Bianchi. International Mathematical Research Notices, 2025.5 (2025), rnaf028.
• A stable splitting of factorisation homology of generalised surfaces (arXiv). Journal of the London Mathematical Society, 111.2 (2025), e70089.
• Computations in the unstable homology of moduli spaces of Riemann surfaces (2022), with Carl-Friedrich Bödigheimer and Felix Boes.
• Parametrised moduli spaces of surfaces as infinite loop spaces (arXiv), with Andrea Bianchi and Jens Reinhold. Forum of Mathematics, Sigma 10, e39 (2022).
• Configuration spaces of clusters as E_d-algebras (arXiv). Homotopy, Homology and Applications 26.1 (2024), pp. 319–339.
• Vertical configuration spaces and their homology (arXiv), with Andrea Bianchi. Quarterly Journal of Mathematics 73.4 (2022), pp. 1279–1306.

Courses

• Topics in Algebraic Topology. Lecture notes for a master course (6 ECTS) I gave in summer 2025 at the KIT. The course was accompanied by a set of exercises.
• Kategorientheorie: Grundlagen. Lecture notes (German) for a course I gave at the CdE-WinterAkademie 2023 · 24. The course was accompanied by a set of exercises.

Theses

• Coloured topological operads and moduli spaces of surfaces with multiple boundary curves. PhD 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.