I consider myself an algebraic topologist working at the intersection with arithmetic/algebraic geometry. Here I use tools from higher category theory, homotopy theory and condensed mathematics.
“Condensed Mathematics” is an alternative approach to topology developed by Clausen-Scholze in 2018–2019. At the same time, Barwick, Glasman, and Haine arrived at the same idea under the name “Pyknotic Mathematics.” The theory overcomes shortcomings of the classical point-set topology approach that arise when algebraic structures are equipped with a topology.
Homotopy theory deals with the study of all kinds of spaces using algebraic invariants such as homotopy groups. Very often, these invariants are inherently equipped with a topology. My work aims to perform homotopy theory within the framework of condensed mathematics. In particular, I am interested in defining and studying refined homotopy-theoretic invariants using the setting of condensed mathematics. The objects of interest range from classical topological spaces to spaces that play a fundamental role in algebraic and arithmetic geometry, such as schemes, adic spaces, and rigid analytic spaces.
Apart from that I am eager to learn more about other areas of algebraic topology.
Papers and Preprints
Animated condensed sets and their homotopy groups (preprint), 2021, arXiv:2105.07888
The condensed homotopy type of a scheme (preprint), 2025, arXiv:2510.07443, joint with Peter Haine, Tim Holzschuh, Marcin Lara, Louis Martini, Sebastian Wolf
The Role of Condensed Mathematics in Homotopy Theory, 2025, (Dissertation)
Shape theory for condensed anima (preprint), 2026, arXiv:2605.07843
On Galois categories and condensed contractibe schemes (preprint), 2026, arXiv:2605.10358
Ongoing Projects
The condensed homotopy type of a rigid space, joint with Piotr Achinger, Peter Haine, Tim Holzschuh, Marcin Lara, Sebastian Wolf
Applications of homotopical combinatorics to model category structures, joint with Kristina Dengler, Sofía Martínez Alberga, Kristen Mazur, Constanze Roitzheim, Rehka Santhanam, in the occasion of the Women in Topology (WiT) V workshop