Research interests

My research concerns algebraic and quantum topology. In particular, I focus on 4-dimensional homotopy quantum field theories (a generalization of topological quantum field theories) and homotopy 3-types.

Thesis project: Homotopy field theories and 3-types

Quantum topology is a field that came about in the 1980s following remarkable discoveries by Jones, Drinfeld and Witten whose work (recognized by Fields medals awarded to each of them in 1990) dramatically renewed topology, in particular in low dimension. A fundamental notion in quantum topology is that of topological quantum field theory (TQFT) formulated by Witten. This notion originates in ideas from quantum physics and constitutes a framework that organizes certain topological invariants of manifolds, called quantum invariants, which are defined by means of quantum groups. Homotopy quantum field theories (HQFTs) are a generalization of TQFTs. The idea is to use TQFT techniques to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a topological space X. 

Turaev and Virelizier have constructed 3-dimensional HQFTs (by state-sum) when the space X is aspherical (i.e. its n-th homotopy groups of X are trivial for n>1) and Sözer and Virelizier have constructed 3-dimensional HQFTs when X is a 2-type (i.e. its n-th homotopy groups are trivial for n>2). Using state sum techniques, Douglas and Reutter constructed 4-dimensional TQFTs from spherical fusion 2-categories. The aim of this PhD project is to generalize these constructions (both from the topological and the algebraic viewpoint) to the case of 4-dimensional HQFTs with target a 3-type. In this case, the relevant algebraic structures for constructing such HQFTs should be spherical fusion 2-categories graded by a 2-crossed module.

Talks

• (future) Feb 2026 - Algebraic Topology seminar, UCLouvain

• (future) Feb 2026 - Topology seminar, Université de Lille

• Nov 2025 - Quantum Universe Attract. Workshop, Universität Hamburg

• Sep 2025 - Higher Structures: Recent developments and applications, Universität Hamburg (see slides)

• May 2025 - Algebraic Approaches to Mapping Class Groups of Surfaces, The University of Tokyo

• May 2025 - FJ-LMI Seminar, The University of Tokyo (see slides)

• Apr 2025 - Journées de Jeunes Chercheuses et Chercheurs en Topologie, Université Picardie Jules Verne

• Nov 2024 - Séminaire des doctorants et post-doctorants, Université de Lille (see slides in French)

• Jan 2024 - Topology seminar, University of Louisiana at Lafayette (see slides)

• Sep 2023 - Topology seminar, Université de Lille

Conferences attended

• (future) Mar 2026 - Journées de topologie algébrique, géométrique et quantique en Picardie III, Université Picardie Jules Verne

• (future) Mar 2026 - Winter braids XV, Aix-Marseille Université

• Oct 2025 - Journée de topologie quantique, Université Paris-Cité

• Sep 2025 - Higher Structures: Recent developments and applications, Universität Hamburg

• May 2025 - Algebraic approaches to mapping class groups of surfaces,  The University of Tokyo

• Apr 2025 - Journées de Jeunes Chercheuses et Chercheurs en Topologie, Université Picardie Jules Verne 

• Mar 2025 - Journées de topologie algébrique, géométrique et quantique en Picardie II, Université Picardie Jules Verne

• Feb 2025 - Winter braids XIV, Université de Bordeaux

• Dec 2024 - Skein days, Journées thématiques de Cergy-Pontoise, CY Cergy Paris Université

• Nov 2024 - Journée de topologie quantique, Université Paris-Cité 

• Oct 2024  - Séminaire itinérant de catégories, Université Paris-Cité

• Oct 2024 - Higher structures in Noncommutative Geometry and Quantum Algebra, Université de Lille

• Sep 2024 - Scottish Talbot on Algebra and Topology, Cairngorm Lodge, Glenmore, Scotland

• Apr 2024 - Séminaire itinérant de catégories, Université de Lille

• Mar 2024 - Journées de topologie algébrique, géométrique et quantique en Picardie, Université Picardie Jules Verne

• Mar 2024 - Journée de topologie quantique, Université Paris-Cité

• Feb 2024 - Winter braids XIII, Université de Montpellier 

• Oct 2023 - Conférence du GDR Théorie de l'Homotopie et Applications, Université de Lille

• Oct 2023 - Séminaire itinérant de catégories, Université du Littoral à Calais

• Mar 2023 - Building-up differential homotopy theory at Aizu, The University of Aizu

• Feb 2023 - 18th East Asian Conference on Geometric Topology, online

• Nov 2022 - International conference on "Topology and its Applications to Engineering and Life Science", online

Mathematical projects

Notes

• "Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology", 2025

• "Constructions of 2-holonomy functors", ARPE report, 2023, under the supervision of Toshitake Kohno

• "Sur la topologie des surfaces algébriques réelles non singulières de degré au plus 5 dans RP^3", master's thesis, 2022 (in French), under the supervision of Ilia Itenberg

• "The invariance of knot lattice homology", first year master's project, 2021

Interdisciplinary projects

• "Contrefaçon d'une œuvre musicale : comment déterminer le plagiat ?", research project in law and mathematics, 2023, with Thomas Hum (see poster)