I am a fourth year PhD student at the Mathematical Institute of the
University of Bonn under the supervision
of Carl-Friedrich
Bödigheimer, in the area of algebraic topology. I am funded by the Max
Planck Institute for Mathematics in Bonn and am a member of
the International Max Planck research school (
My PhD project deals with coloured topological operads and their algebras, configuration spaces, and the phenomenon of homological stability, as well as mapping class groups, moduli spaces of Riemann surfaces and their homology.
More recently, I have been studying low-dimensional equivariant and parametrised cobordism categories and their homotopy type.
My co-authors are Andrea Bianchi from the University of Copenhagen and Jens Reinhold from the University of Münster.
In the summer term 2020, I co-organised a graduate seminar on Operads in Algebra and Topology together with Andrea Bianchi. Moreover, I have been tutor for the following topology lectures:
summer 2021 | Algebraic Topology 2 | Carl-Friedrich Bödigheimer |
winter 2020/21 | Algebraic Topology 1 | Carl-Friedrich Bödigheimer |
summer 2020 | Algebraic Topology 2 | Christoph Winges |
winter 2019/20 | Algebraic Topology 1 | Wolfgang Lück |
summer 2019 | Topology 2 | Daniel Kasprowski |
winter 2018/19 | Topology 1 | Wolfgang Lück |
summer 2018 | Geometrie und Topologie | Wolfgang Lück |
We study the E_{2}-algebra
\(\Lambda\mathfrak{M}\)
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 \(\Omega B\Lambda\mathfrak{M}\): it is the product of
\(\Omega^\infty\mathbf{MTSO}(2)\) with a certain free
It is a classical result that configuration spaces of labelled particles
in \(\mathbb{R}^d\) are free algebras over the little
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.
This is my master’s thesis which was finished in the summer term 2018. Its main result is a Poincaré–Lefschetz correspondene between the Mumford–Miller–Morita classes in the cohomology of moduli spaces and certain simplicial subcomplexes of Bödigheimer’s model of parallel slit domains.
These are the notes of a talk I gave in the winter term 2020/21 in our
In summer 2020, the first ‘corona term’, I gave an introductory talk on
model categories in our
Mathematical Institute
Office 4.020
Endenicher Allee 60
53115 Bonn
Germany
0xD2890F65
)