Research interests

My research concerns algebraic and quantum topology. In particular, I focus on a 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. 3-dimensional HQFTs have recently been constructed (by state-sum) when the space X is aspherical (i.e. the n-th homotopy groups of X are trivial for n>1) and when X is a 2-type (i.e. its n-th homotopy groups are trivial for n>2). The aim of this PhD project is to generalize (both from the topological and the algebraic viewpoint) these constructions to the case where X is a 3-type. In this case, the relevant algebraic structures for constructing such HQFTs should be fusion 2-categories graded by a quadratic module.

Talks and conferences

Talks given

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

• 29 September 2023 - Université de Lille, Topology seminar

Conferences attended

• 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 - Winterbraids 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