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.
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).
University of Hamburg · Supervisor: David Reutter · Submitted 23 September 2026
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.
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.