On this page

↪ Research interests
↪ Preprints
↪ Publications and accepted papers
↪ Doctoral thesis
↪ Recordings of talks
↪ More about my research interests: an informal introduction to knot theory

Research interests ⤴

I am interested in low-dimensional topology, which is the branch of topology that studies manifolds of dimension \(4\) and below. In particular, I like to study knots as closures of braids, and I like to think about (non)orientable surfaces embedded in the \(4\)-ball that bound a given knot in the \(3\)-sphere or two such knots, e.g. knot concordances and cobordisms. I also enjoy thinking about braid groups and their Garside structures, knotted surfaces, \(3\)- and \(4\)-manifolds, Khovanov and Heegaard Floer homology. An informal introduction to some of these topics can be found here!

Preprints ⤴

1. The Conway knot has infinite concordance order
   joint with Chiara Donatone, Marc Kegel, Lukas Lewark
   ↪ arXiv:2606.30422
2. On \(\mathcal{T}\)-positive links
   joint with Benjamin Bode
   ↪ arXiv:2605.10502

Publications and accepted papers ↪ arXiv

These are listed in reverse chronological order of acceptance. For a list in reverse chronological order of writing, please refer to my CV on the About me page.

1. On the detection of knots by their traces in high dimensions
   joint with Valentina Bais, Alessio Di Prisa, Daniel Hartman, Chun-Sheng Hsueh, Marc Kegel, Alice Merz, Mark Pencovitch, Arunima Ray, Diego Santoro, Laura Wakelin
   ↪ Proc. London Math. Soc. 133: e70226 (2026).
   ↪ arXiv:2511.07251
2. Strongly quasipositive links are concordant to infinitely many strongly quasipositive links
   ↪ Proc. Amer. Math. Soc. Ser. B 13 (2026), 159–174.
   ↪ arXiv:2210.06612
3. Braid positive surgery diagrams
   joint with Marc Kegel
   ↪ Glasg. Math. J. (2026), 1–6.
   ↪ arXiv:2512.14589
4. Non-complex cobordisms between quasipositive knots
   joint with Maciej Borodzik
   ↪ J. Math. Pures Appl. (9) 207:11 (2026). Id/No 103842.
   ↪ arXiv:2504.04894
5. Algorithms in 4-manifold topology
   joint with Stefan Bastl, Rhuaidi Burke, Rima Chatterjee, Subhankar Dey, Alison Durst, Stefan Friedl, Daniel Galvin, Alejandro García Rivas, Tobias Hirsch, Cara Hobohm, Chun-Sheng Hsueh, Marc Kegel, Frieda Kern, Shun Ming Samuel Lee, Clara Löh, Naageswaran Manikandan, Léo Mousseau, Lars Munser, Mark Pencovitch, Patrick Perras, Mark Powell, José Pedro Quintanilha, Lisa Schambeck, David Suchodoll, Martin Tancer, Annika Thiele, Matthias Uschold, Simona Veselá, Melvin Weiß, Magdalina von Wunsch-Rolshoven
   This paper is the result of our joint work at the Workshop on 4-manifolds and algorithms held at the University of Regensburg in September 2024.
   ↪ Algebr. Geom. Topol. 26-8 (2026), 3017–3049.
   ↪ arXiv:2411.08775
   
6. Minimal cobordisms between thin and thick torus knots
   joint with Sebastian Baader, Lukas Lewark, Filip Misev
   ↪ Proc. Edinb. Math. Soc. 69, no. 1 (2026), 177–183.
   ↪ arXiv:2405.13719
   
7. On the nonorientable four-ball genus of torus knots
   joint with Fraser Binns, Sungkyung Kang, Jonathan Simone
   ↪ Algebr. Geom. Topol. 25-4 (2025), 2209–2251.
   ↪ arXiv:2109.09187
   
8. 3-braid knots with maximal 4-genus
   joint with Sebastian Baader, Lukas Lewark, Filip Misev
   ↪ Trans. Amer. Math. Soc. Ser. B 11 (2024), 600–621.
   ↪ arXiv:2303.11918
   
9. The upsilon invariant at \(1\) of \(3\)-braid knots
   ↪ Algebr. Geom. Topol. 23-8 (2023), 3763–3804.
   ↪ arXiv:2108.03674
   

Doctoral thesis ⤴

On notions of braid positivity and knot concordance, ETH Zurich (2023).
Here are the slides from my PhD defense talk, and the slightly uglier but shorter handout version of the slides.

Me defending my PhD thesis in June 2023, photo credit: Lukas Lewark.

Peter Feller was my PhD advisor and Lukas Lewark was my second advisor for the final 1.5 years.

Recordings of talks ⤴

• The Conway knot has infinite concordance order, Young Women in Geometric Topology, Hausdorff Research Institute for Mathematics (HIM), Bonn, July 2026.
  🎥 Recording of my blackboard talk.
• Strongly quasipositive knots are concordant to infinitely many strongly quasipositive knots, The Low-dimensional Workshop, Erdős Center, Alfréd Rényi Institute of Mathematics, Budapest, March 2023.
  🎥 Recording of my blackboard talk and a photo by Sarah Blackwell.
• Strongly quasipositive knots are concordant to infinitely many strongly quasipositive knots, Geometry and Topology Seminar, CIRGET (online), December 2022.
  🎥 Recording of my talk and the slides.
• The alternation number and the Upsilon-invariant at 1 of positive 3-braid knots, Knot online seminar (K-OS) (online), February 2022.
  🎥 Recording of my talk and the slides.

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