Florian Kranhold
Address 
Mathematical Institute University of Bonn Endenicher Allee 60 53115 Bonn 

Room  4.020 
Phone  +49 (0)228 7362208 
PGP Public Key (0xD2890F65) 
I am a PhD student of CarlFriedrich Bödigheimer, expecting to defend my thesis in May 2022. My research interests lie in the area of algebraic topology: more specifically, I am interested in (coloured) topological operads and their algebras, configuration spaces and their homological stability, as well as diffeomorphism groups and mapping class groups, moduli spaces of surfaces and their (unstable) homology. More recently, I have been studying lowdimensional equivariant and parametrised cobordism categories and their homotopy type.
My coauthors are Andrea Bianchi from the University of Copenhagen and Jens Reinhold from the University of Münster.
Here is my CV and my ORCID record, and you can watch a Zoom talk I gave in the Purdue Topology Seminar in September 2021, as well as a Talk at a blackboard I gave at a Workshop in Copenhagen in November 2021.
Preprints

Parametrised moduli spaces of surfaces as infinite loop spaces
12/05/2021, arXiv:2105.05772, Recorded talk, with Andrea Bianchi and Jens Reinhold
We study the \(E_2\)algebra \(\Lambda\mathfrak{M}_{*,1}=\coprod_{g\geqslant 0}\Lambda\mathfrak{M}_{g,1}\) consisting of free loop spaces of moduli spaces of Riemann surfaces with one parametrised boundary component, and compute the homotopy type of the group completion \(\Omega B\Lambda\mathfrak{M}_{*,1}\): it is the product of \(\Omega^\infty\mathbf{MTSO}(2)\) with a certain free \(\Omega^\infty\)space depending on the family of all boundaryirreducible mapping classes in all mapping class groups \(\Gamma_{g,n}\) with \(g\geqslant 0\) and \(n\geqslant 1\).

Configuration spaces of clusters as \(E_d\)algebras
06/04/2021, arXiv:2104.02729, Recorded talk
It is a classical result that configuration spaces of labelled particles in \(\mathbb{R}^d\) are free algebras over the little \(d\)cubes operad \(\mathscr{C}_d\), and their \(d\)fold bar construction is equivalent to the \(d\)fold suspension of the labelling space. The aim of this paper is to study a variation of these spaces, namely the configuration space of labelled clusters of points in \(\mathbb{R}^d\). This configuration space is again an \(E_d\)algebra, but in general not a free one. We give geometric models for their iterated bar construction in two different ways: one uses an additional verticality constraint, and the other one uses a description of these clustered configuration spaces as cellular \(E_1\)algebras. In the last section, we show a stable splitting result and present some applications.

Vertical configuration spaces and their homology
22/03/2021, arXiv:2103.12137, with Andrea Bianchi
We introduce ordered and unordered configuration spaces of ‘clusters’ of points in an Euclidean space \(\mathbb{R}^d\), where points in each cluster have to satisfy a ‘verticality’ condition, depending on a decomposition \(d=p+q.\) We compute the homology in the ordered case and prove homological stability in the unordered case.

Moduli spaces of Riemann surfaces and symmetric products: A combinatorial description of the Mumford–Miller–Morita classes
25/09/2018, PDF (911 kiB)
This is my master thesis which was finished in the summer term 2018 under the supervision of CarlFriedrich Bödigheimer. Its main result is a Poincaré–Lefschetz correspondence between the Mumford–Miller–Morita classes in the cohomology of moduli spaces and certain subcomplexes of Bödigheimer’s simplicial model of parallel slit domains.
Teaching
In the summer term 2022, I am the teaching assistant for the lectures Einführung in die Geometrie und Topologie by Koen van den Dungen and Topology 2 by Daniel Kasprowski.
In the summer term 2020, I coorganised a graduate seminar on Operads in Algebra and Topology together with Andrea Bianchi. Moreover, I have been tutor for the following topology lectures:
SoSe 2021  Algebraic Topology 2  CarlFriedrich Bödigheimer 
WiSe 2020/21  Algebraic Topology 1  CarlFriedrich Bödigheimer 
SoSe 2020  Algebraic Topology 2  Christoph Winges 
WiSe 2019/20  Algebraic Topology 1  Wolfgang Lück 
SoSe 2019  Topology 2  Daniel Kasprowski 
WiSe 2018/19  Topology 1  Wolfgang Lück 
SoSe 2018  Einführung in die Geometrie und Topologie  Wolfgang Lück 
News
Corona: Measures at the Center for Mathematics
24.6.22: Colloquium on occasion of the retirement of Herrn Prof. Dr. CarlFriedrich Bödigheimer
Prof. Peter Scholze elected as Foreign Member of the Royal Society
Prof. Dr. Jessica Fintzen new at the Mathematical Institute
Otto Toeplitz memorial fund established
Hausdorff Memorial Prize 2020/2021 awarded
Bachelorpreis 2020/21 der BMG verliehen
Prof. Christoph Thiele is holding the Clay Lecture 2022
Hausdorff Edition „Felix Hausdorff  Gesammelte Werke“
Prof. Catharina Stroppel invited as plenary speaker to the ICM 2022 in St. Petersburg
Bonner Mathematik belegt bei Shanghai Ranking den 1. Platz in Deutschland und weltweit den 13. Platz
Prof. Georg Oberdieck erhält Heinz MaierLeibnitzPreise 2020
Prof. Daniel Huybrechts erhält gemeinsam mit Debarre, Macri und Voisin ERC Synergy Grant