I am a PhD researcher at the University of Hamburg, working with David Reutter. I work on higher category theory, homotopy theory, and extended topological field theories.
I submitted my thesis, Cauchy-completions and higher fusion categories, in September 2026.
In November 2026, I will join the Max Planck Institute for Mathematics in Bonn.
An enriched ∞-operad can be recovered from its category of right modules, together with a marking by the representable ones. This reduces their study to the theory of presentably symmetric monoidal module categories. I use this description to prove, for enrichment in spaces, an equivalence between algebras in symmetric sequences and Lurie’s definition of ∞-operads, that also identifies the respective categories of algebras.
We prove that an enriched ∞-category is determined by its enriched presheaf category, together with a marking by the representable presheaves. This description reduced enriched ∞-category theory to the study of presentable module categories. For instance, we recover the tensor product of enriched categories from the cocompleted tensor product on presentable categories, and give a very model-independent account of univalence (Rezk-completeness).
Also: Higher tensor categories and their extensions — joint Scottish Talbot notes (2025).
My thesis studies higher fusion categories using enriched ∞-category theory. More precisely, it characterizes the Morita category of separable multifusion categories as a higher Cauchy-completions of the trivial k-linear n-category B^n k, and shows that it consists of precisely the fully dualizable objects in the Morita-category of n-idempotent-complete k-linear n-categories.
The main result shows that higher idempotent-completion preserves adjoints at all categorical levels. By the Cobordism Hypothesis, the resulting fully dualizable objects determine fully extended framed topological field theories.
Abstract and thesis detailsMy main interests are in higher category theory and its applications to topology and mathematical physics.
I study enriched ∞-categories and ∞-operads, including their descriptions through marked presentable categories. Other aspects of my work include weighted colimits, profunctors, and Cauchy-completion.
I study higher fusion categories and their relation to extended topological field theories. My work uses higher Cauchy-completion to characterize these categories and establish full dualizability.
I am interested in constructible sheaves, Verdier duality, and the algebraic L-groups of stratified spaces, including their relation to stratified surgery theory.
I study the relationship between the BV formalism and constructible factorization algebras, and how these constructions extend from manifolds to stratified spaces.
| Time | Name | Place |
|---|---|---|
| 11.–15.08.2025 | Masterclass: Infinity Operads and Applications to Geometry | Copenhagen, Denmark |
| 20.–27.07.2025 | Conference: Spaces of Tensor Categories | Edinburgh, Great Britain |
| 29.06.–05.07.2025 | European Talbot — Higher algebra and chromatic homotopy theory | Kolding, Denmark |
| 24.–27.02.2025 | Workshop on Gray Products and Lax Constructions | Raitenhaslach, Germany |
| 16.–21.02.2025 | Cobordism categories Masterclass: Building bridges between algebra and geometry | Copenhagen, Denmark |
| 22.–28.09.2024 | Scottish Talbot On Algebra and Topology - "Higher tensor categories and their extensions" | Glenmore, Scotland |
| 09.-13.09.2024 | Workshop on "Dualisable Categories & Continuous K-theory" | Bonn, Germany |
| 10.-14.06.2024 | Masterclass: Continuous K-theory, dualizable and rigid categories | Copenhagen, Denmark |
| 15.-19.04.2024 | (∞,n)-Categories and their applications | Utrecht, Netherlands |
| 08.-09.04.2024 | Bavarian Geometry & Topology Meeting XII | Regensburg, Germany |
| 19.01.2024 | 16th Seminar on Conformal Field Theory | Darmstadt, Germany |
| 18.-22.09.2023 | Conference on Characteristic Classes and Singular Spaces | Kiel, Germany |
| 14.-18.08.2023 | Higher Structures in Functorial Field Theory | Regensburg, Germany |
| 19.-23.06.2023 | Hausdorff School: TQFTs and their connections to representation theory and mathematical physics | Bonn, Germany |
| 22.-24.03.2023 | Higher categorical methods in algebra and geometry | Hamburg, Germany |
| 18.-22.07.2022 | Domoschool 2022: Gauge Theory and the Langlands Program | Domodossola, Italy |
| 04.-08.10.2021 | Pure Spinors, Superalgebras, and Holomorphic Twists | Heidelberg, Germany |
| 12.-16.07.2021 | Junior Researchers Conference: Higher Structures in QFT and String Theory | Online |
From November 2026
Max Planck Institute for Mathematics, Bonn