Research
My main research interests are algebraic rewriting and categorification in representation theory. My objective is to develop efficient tools based on rewriting theories to study diagrammatic algebras and categories arising in categorification problems. In particular, my goal is to develop tools based on rewriting modulo the axioms of the inherent algebraic structure to automatize the computation of linear bases, coherent presentations, cofibrant replacements, etc.
Publications
- Coherent confluence modulo relations and double groupoids, avec P. Malbos, Journal of Pure and Applied Algebra , Volume 226, Issue 10, October 2022, 107037. arXiv, PDF.
- Rewriting modulo in pivotal linear (2,2)-categories, Journal of Algebra , 2022, Volume 601, 1 July 2022, Pages 1-53. arXiv, PDF.
- Confluence of algebraic rewriting systems , avec C. Chenavier et P. Malbos, Mathematical Structures in Computer Science, special issue on Confluence, 2021, pages 1-28. arXiv, PDF.
- Rewriting modulo isotopies in Khovanov-Lauda-Rouquier's categorification of quantum groups, Advances in Mathematics, Volume 378, Feb. 2021, 107524. arXiv , PDF
Preprints
- Categorification of infinite-dimensional sl2-modules and braid-group 2-actions I: tensor products , 2021, avec G. Naisse, arXiv, PDF, submitted.
- Super rewriting theory and nondegeneracy of odd categorified sl(2), 2021, avec M. Ebert et A. Lauda, arXiv, PDF, submitted.
Abstracts and talks in international conferences
- International Workshop on Confluence, Buenos Aires, 2021, Completion of operadic rewriting systems by Gaussian elimination , (avec Philippe Malbos et Isaac Ren). Abstract. Slides.
- International Workshop on Confluence, Paris, 2020, Algebraic critical pair lemma , (avec Cyrille Chenavier et Philippe Malbos). Abstract. Slides.
- Category Theory, Edimburgh, 2019, Coherence modulo and double groupoids. Slides
- Second sympositum on compositional structures (SYCO 2), Glasgow, 2018, Diagrammatic rewriting modulo isotopy. Abstract. Slides.
- Workshop LHC (Logique, Homotopie, Catégories), Marseille, 2018, Coherence modulo relations and double groupoids (avec Philippe Malbos). Slides.
- International workshop on confluence, Oxford, 2018, Coherence modulo relations (avec Philippe Malbos). Abstract. Slides.
- Workshop Higher dimensional rewriting and applications, Oxford, 2018, Termination in linear (2,2)-categories with braidings and duals. Abstract. Slides.
- Workshop GeoCal, Nantes, 2017, Higher-dimensional linear rewriting. Slides.
- Workshop Higher dimensional rewriting and applications, Oxford, 2017, A convergent presentation for the simply-laced KLR algebra and the PBW property. Abstract. Slides.
Seminars
- Algebraic rewriting seminar, online, 2021: Diagrammatic rewriting and categorification.
- Séminaire AGATA, Institut Montpelliérain Alexander Grothendieck, 2021: Calcul de bases dans des 2-catégories linéaires par réécriture.
- Categorification Learning Seminar, online, 2021: Computing bases in linear 2-categories using rewriting theory.
- Séminaire d'algèbre, Université Claude Bernard Lyon 1, 2020: Bases dans des 2-catégories linéaires par réécriture.
- Séminaire de mathématiques, Université de Reims, 2020: Bases dans des 2-catégories linéaires par réécriture.
- Séminaire d'algèbre, Université d'Ottawa, 2019: Finding bases in linear categories using rewriting.
- Journée équipe AGL, Université Lyon 1, 2019: Réécrire dans les algèbres diagrammatiques.
- Séminaire des doctorants et doctorantes, Université Lyon 1, 2018: La réécriture algébrique.
PhD Thesis
- Manuscript of my PhD Thesis entitled Rewriting modulo in diagrammatic categories . Slides of the defense.
Posters
- International School on Rewriting, Eindhoven, 2017: Rewriting on string diagrams and categorification.
- Journées du GdR IM, Palaiseau, 2018: Higher-dimensional linear rewriting.
Talks in workshops
- Introduction to knot theory, polynomial invariants and Khovanov homology, Université Claude Bernard Lyon 1, Groupe de travail sur groupes de tresses, in french.
