Florian Kranhold: Mathematics

My mathematical interests lie in the area of Algebraic and Geometric Topology. More specifically, I like to think about configuration spaces and topological moduli spaces, operads, factorisation homology, and bordism categories.

Research articles

Segal K-theory of vector spaces with an automorphism (with Andrea Bianchi). International Mathematical Research Notices (5 2025), rnaf028 [DOI, arXiv].
A stable splitting of factorisation homology of generalised surfaces. Journal of the London Mathematical Society, 111.2 (2025), e70089 [DOI, arXiv].
Configuration spaces of clusters as E_d-algebras. Homology, Homotopy and Applications 26.1 (2024), pp. 319–339 [DOI, arXiv].
Computations in the unstable homology of moduli spaces of Riemann surfaces (with Carl-Friedrich Bödigheimer and Felix Boes). Preprint, 2022 [arXiv].
Parametrised moduli spaces of surfaces as infinite loop spaces (with Andrea Bianchi and Jens Reinhold). Forum of Mathematics, Sigma 10 (2022), e39 [DOI, arXiv].
Vertical configuration spaces and their homology (with Andrea Bianchi). Quarterly Journal of Mathematics 73.4 (2022), pp. 1279–1306 [DOI, arXiv].

Teaching materials

Topics in Algebraic Topology. A master’s course I taught at KIT in the summer term of 2025 [notes, exercises].
Kategorientheorie: Grundlagen. An introductory course I taught at the CdE-WinterAkademie 2023·24 (in German) [notes, exercises].

Theses

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