Young Research Groups (YRG) are offered for up to four years and consist of two or three postdocs, who work jointly on an independent project relevant to the research programme of Mathematics Münster. Here we list all funded YRGs of Mathematics Münster.
Since 2023
Understanding the cohomology of arithmetic groups such as $\operatorname{SL}_n(\mathbb{Z})$ or $\operatorname{Sp}_{2n}(\mathbb{Z})$ is a fundamental problem, which connects many areas of mathematics. It is motivated by questions in number theory, has applications in algebraic K-theory, and is closely related to the cohomology of moduli spaces such as $\mathcal{A}_g$.
However, computing these invariants is notoriously difficult - even in the simplest case: the rational cohomology. Low cohomological degrees are accessible by classical homological stability techniques and computer calculations, but little is known in high degrees.
The goal of this Young Research Group is to study these high-degree rational cohomology groups for a well-behaved class of arithmetic groups, namely Chevalley groups $\mathcal{G}_n(\mathcal{O})$ for $\mathcal{O}$ the ring of integers of a number field $\mathbb{K}$, such as $\operatorname{SL}_{n+1}(\mathcal{O})$, $\operatorname{\mathbb{P}GL}_{n+1}(\mathcal{O})$, $\operatorname{Spin}_{2n+1}(\mathcal{O})$, $\operatorname{Sp}_{2n}(\mathcal{O})$, and $\operatorname{SO}_{2n}(\mathcal{O})$. In particular, we investigate the following generalization of a conjecture by Church-Farb-Putman: $H^{\operatorname{vcd} - i}(\mathcal{G}_n(\mathcal{O});\mathbb{Q}) = 0$ if $i \leq n-1$, where $\mathcal{O}$ is Euclidean and $\operatorname{vcd}$ denotes the virtual cohomological dimension of $\mathcal{G}_n(\mathcal{O})$.
"I completed both my Bachelor's and Master's degrees in Münster. During my Master's, I spent half a year in Lyon, where I also wrote my Master's thesis on a topic at the intersection of model theory and geometric group theory. Afterwards, I did my doctorate in Bielefeld under the supervision of Kai-Uwe Bux, focusing primarily on topics in geometric group theory. In particular, I studied automorphisms of free groups and right-angled Artin groups.
Following my doctorate, I held postdoctoral positions in Copenhagen and then at ETH Zurich. During this time, I mainly worked on topological properties of groups and began collaborating with Robin. I also pursued a few projects in topological data analysis, some in collaboration with a group of astrophysicists.
Since autumn 2023, I have been based in Münster, where I hold a fixed-term position as Akademischer Rat (lecturer with research duties) at the Institute for Mathematical Logic and Foundations of Mathematics. Since winter 2024, I have been an investigator at the Cluster of Excellence Mathematics Münster."
"My research explores patterns in (co)homological invariants of groups and algebras, often in relation to questions in (algebraic) K-theory. This usually relies on a good understanding of combinatorial geometries and simplicial structures on which the groups and algebras act.
I began working on such questions as an exchange student at Université Paris-Sud, where I completed a summer project about automorphism groups of free groups that eventually inspired my Master's thesis. After returning to Münster and earning my Master's degree, I moved to Copenhagen to start my PhD under the supervision of Nathalie Wahl. My PhD thesis mainly concerned the homology of abstract algebras. Furthermore, it contained a first version of my work with Benjamin Brück and Peter Patzt exploring the cohomology of symplectic groups. After completing my PhD, I was a Junior Fellow at Institut Mittag-Leffler in Sweden and worked with Ian Hambleton at McMaster University in Canada as a Postdoc.
Since September 2023, I am a Postdoctoral Research Associate at the University of Münster working within the research group 'K-Groups and cohomology'. In November 2024, I became an investigator at the Cluster of Excellence Mathematics Münster."