I am a postdoctoral fellow at the Max Planck Institute for Mathematics (Bonn, Germany). My mentor is Catharina Stroppel.
Previously, I was a graduate student at the UCLouvain (Belgium), working under the supervision of Pedro Vaz. I received my PhD in September 2024.
You can find a list of my arXiv preprints here.
Contact: lastname(at)mpim-bonn.mpg.de (lastname=schelstraete)
News
Last update: July 21 2025
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An updated version of "odd Khovanov homology and higher representation theory" is available below.
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My new preprint "A basis and Schur–Weyl duality for the loop Hecke algebra" is out! Joint with Geoffrey Janssens, Abel Lacabanne and Pedro Vaz, arXiv:2507.12839.
Research interests
Keywords: low-dimensional topology (Khovanov homology), representation theory (categorification, quantum groups) and rewriting theory (diagrammatic algebras, higher Göbner bases, higher category theory).
On the one hand, I study quantum invariants of knots related to the representation theory of quantum groups. Both sides can be categorified: as homological invariants for the former (e.g. Khovanov homology) and as diagrammatic algebras for the latter (e.g. KLR algebras). I am interested in their interaction as well as their connection with various other fields. My recent research has focused on the "oddification" of this story; intuitively, moving form commutativity to anti-commutativity. This features odd Khovanov homology on the topological side, and super algebraic structures on the representation theoretic side, as in 2311.14394.
On the other hand, I am interested in rewriting theory (the algorithmic study of presented algebraic structures) and its applications to diagrammatic algebras, categorification and quantum topology. In arXiv:2502.03028, I developed a theory of higher linear rewriting, sufficiently flexible to deal with diagrammatic algebras as they appear in practice; one may think of it as a higher notion of Gröbner bases, or as a higher notion of Bergman's diamond lemma. In the same work, I applied the theory to a basis problem appearing in quantum topology. I am currenctly working in extending the realm of applicability of the theory.
Publications and preprints
Preprints:
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A basis and Schur–Weyl duality for the loop Hecke algebra, joint with Geoffrey Janssens, Abel Lacabanne and Pedro Vaz, arXiv:2507.12839
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Rewriting modulo in diagrammatic algebras and application to categorification, arXiv:2502.03028, submitted
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Odd khovanov homology and higher representation theory, joint with Pedro Vaz, arXiv:2311.14394, submitted (see here for a more up-to-date version)
Thesis:
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Odd khovanov homology, higher representation theory and higher rewriting theory, arXiv:2410.11405, 2024, PhD thesis
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Supercategorification and Khovanov-like tangle invariants, 2020, Master Thesis, available here
Previously
Research talks
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Réécriture linéaire supérieure dans les algèbres diagrammatiques, Lyon, June 26
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A novel approach to odd Khovanov homology, May 22, Hamburg
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Rewriting methods in diagrammatic algebras, Tallinn, April 7-11
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Rewriting in diagrammatic algebras, Bonn, December 2024
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Oddification, de la théorie des représentations à la topologie, Marseille, November 14 2024
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Réécriture en algèbre supérieure et applications, Montpellier, November 13 2024
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Oddification, from representation theory to topology, Bochum, November 7 2024
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A novel approach to odd Khovanov homology, Max Planck Institute of Mathematics, low-dimensional topology seminar, October 22 2024
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Oddification, from representation theory to topology, University of Bonn, algebra seminar, October 11 2024
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Odd Khovanov homology and higher representation theory,
Clermont-Ferrant, May 28 2024
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Odd Khovanov homology and higher representation theory, EQuAL seminar, May 23 2024 (notes)
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Odd Khovanov homology and higher representation theory, University of Oregon, algebra seminar, January 2024
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Odd Khovanov homology and higher representation theory, JMM 2024: Special Session on Knots, Skein Modules, and Categorification, San Francisco, January 2024 (slides)
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Odd Khovanov homology and higher representation theory,
Winter Braids in Tours, February 2023
(slides, link)
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Odd Khovanov homology and 2-supercategories,
UCL-ULB-VUB seminar on quantum groups, Hopf algebras and monoidal categories, May 2022
(slides, link)
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Odd Khovanov Homology and Supercategorification,
Winter Braids in Dijon, December 2021
(poster)
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Supercategorification and odd Khovanov homology,
séminaire de topologie algébrique in UCLouvain, October 2020
(slides, link)
Expository talks
A selection of my expository talks:
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Out of line: a leisure tour on two-dimensional calculus, UCLouvain, Junior Colloquium, September 25 2024
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Comment calculer en deux dimensions ?, Université libre de Bruxelles, BSSM 2024, August 29 2024
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Strictification and Gray categories, Junior Category Theory Seminar, UCLouvain, February 2024, companion notes
Travel
2024
2023
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LMS-Bath Summer School on Geometric and Categorical Representation theory, Bath, August 2023
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Hecke algebras and applications, Spetses, July 2023
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Workshop on Seiberg-Witten theory, Matemale, June 2023
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Winter Braids XII, Tours, February 2023
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BTW3: Morse and Floer theories, Marseille, January 2023
2022
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Climathics, Les Diablerets, November 2022
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Research School on Bicategories, Categorification and Quantum Theory, Leeds, July 2022
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From Subfactors to Quantum Topology - In memory of Vaughan Jones, Geneva, June 2022
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Quantum Topology and Geometry: conference in honor of Vladimir Turaev, Paris, June 2022
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BTW2: Sliceness, exotic pairs, and quantum invariants, Aussois, April 2022
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Recent developments in Link Homology, Les Diablerets, January 2022
2021
