I am a PhD-student at the University of Bonn, supervised by Stefan Schwede. My research is currently focused on equivariant homotopy theory, I am especially interested in questions surrounding equivariant bordism and applications of parametrized category theory to equivariant homotopy theory. From April-July 2026, I am visiting the Copenhagen Centre for Geometry and Topology.
Preprints
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Condensed Group Cohomology (pdf, arXiv)
Condensed mathematics as developed by Clausen and Scholze yields a version of derived functors over the category of continuous G-modules for a Hausdorff topological group G. We study the resulting notion of group cohomology and its relation to continuous group cohomology and the condensed/sheaf/singular cohomology of classifying spaces. While condensed group cohomology is generally a more refined invariant than continuous group cohomology, we show that for a broad class of topological groups, continuous group cohomology with solid coefficients, such as locally profinite continuous G-modules, can be realized as a derived functor in the condensed setting. We also revisit cornerstones of condensed mathematics, paying special attention to set-theoretic size issues. To this end, we review a framework for working with accessible (hyper)sheaves on large sites satisfying suitable accessibility conditions and show that the associated categories retain many topos-like properties. Moreover, we generalize identifications of condensed with sheaf cohomology obtained by Clausen and Scholze.
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Global \(\infty\)-categories and Global Thom Spectra, (pdf, poster)
We introduce a framework of (Lie-)global $\infty$-categories, which formalizes various families of $\infty$-categories indexed by compact Lie groups and equipped with suitable restriction functors along continuous group homomorphisms that occur naturally in equivariant homotopy theory and representation theory. As our main results, we show that in this framework unstable and stable equivariant and global homotopy theory admit universal properties. In particular, we characterize the passage from unstable to stable equivariant and global homotopy theory at the level of global $\infty$-categories as universally inverting the action of representation spheres in an appropriate sense. Building on this, we define parametrized equivariant and global Thom spectrum functors and show that they recover classical Thom spectrum constructions defined in terms of pointset models.