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 and conferences

Talks given

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

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

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

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

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

• 29 September 2023 - Université de Lille, Topology seminar

Conferences attended

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

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

• March 2025 - Topologie algébrique, géométrique et quantique en Picardie II, Université Picardie Jules Verne

• February 2025 - Winter braids XIV, Université de Bordeaux

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

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

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

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

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

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

• March 2024 - Topologie algébrique, géométrique et quantique en Picardie, Université Picardie Jules Verne

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

• February 2024 - Winter braids XIII, Université de Montpellier 

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

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

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

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

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

Where can you find me?

• ORCID

• Google scholar

• ArXiv