Research
Research
I'm interested in knot theory and low-dimensional topology. More precisely, I work with Khovanov homology and the categorification of quantum link invariants and their topological applications.
I'm interested in knot theory and low-dimensional topology. More precisely, I work with Khovanov homology and the categorification of quantum link invariants and their topological applications.
Monoidal 2-categories from foam evaluation - joint with Leon J. Goertz and Paul Wedrich, 2026.
arXiv: https://arxiv.org/abs/2602.11120
In this paper we describe a general framework for constructing examples of locally linear semistrict monoidal 2-categories covering many examples appearing in link homology theory. The main input datum is a closed foam evaluation formula. As examples, we rigorously construct semistrict monoidal 2-categories based on gl(N)-foams, which underlie the general linear link homology theories, and further examples based on Bar-Natan's decorated cobordisms, related to Khovanov homology. These monoidal 2-categories are typically non-semisimple, have duals for all objects, adjoints for all 1-morphisms, and carry a canonical spatial duality structure expressing oriented 3-dimensional pivotality and sphericality.
Khovanov homology and refined bounds for Gordian distances - joint with Lukas Lewark and Claudius Zibrowius, 2024.
arXiv: https://arxiv.org/abs/2409.05743
From Khovanov homology, we extract a new lower bound for the Gordian distance of knots, which combines and strengthens the previously existing bounds coming from Rasmussen invariants and from torsion invariants. We also improve the bounds for the proper rational Gordian distance.
Computing the symmetric gl1-homology - 2023.
Algebraic & Geometric Topology (accepted for publication)
arXiv: https://arxiv.org/abs/2309.16371
The symmetric gln-homologies, introduced by Robert and Wagner, provide a categorification of the Reshetikhin–Turaev invariants corresponding to symmetric powers of the standard representation of quantum gln. Unlike in the exterior setting, these homologies are already non-trivial when n = 1. Moreover, in this case, their construction can be greatly simplified. Our first aim is giving a down-to-earth description of the non-equivariant symmetric gl1-homology, together with relations that hold in this setting. We then find a basis for the state spaces of graphs, and use it to construct an algorithm and a program computing the invariant for uncolored links.
Khovanov homology and rational unknotting - joint with Damian Iltgen and Lukas Lewark, 2021.
arXiv: https://arxiv.org/abs/2110.15107
Building on work by Alishahi-Dowlin, we extract a new knot invariant λ ≥ 0 from universal Khovanov homology. While λ is a lower bound for the unknotting number, in fact more is true: λ is a lower bound for the proper rational unknotting number (the minimal number of rational tangle replacements preserving connectivity necessary to relate a knot to the unknot). Moreover, we show that for all n ≥ 0, there exists a knot K with λ(K) = n. Along the way, following Thompson, we compute the Bar-Natan complexes of rational tangles.
Here you can find my Ph.D. thesis, supervised by Louis-Hadrien Robert and Emmanuel Wagner.
Here you can find my master's thesis, supervised by Lukas Lewark (University of Regensburg).