Research

My research lies at the interface of category theory, differential geometry and mathematical physics, with an algebraic and structural orientation. This page presents my main lines of work in slightly more detail than the home page.

Equivariant 2-Poisson algebra bundles over configuration spaces

I study equivariant algebraic structures over configuration spaces, which parametrise the possible positions of a fixed number of points on a given manifold. These spaces appear naturally in field theory, where they geometrically encode configurations of particles or the supports of local observables.

My current work constructs equivariant 2-Poisson algebra bundles over these spaces. The 2-Poisson condition is the structure that ensures the existence of an underlying Poisson algebra, suitable for quantisation. The construction is inspired by the algebraic framework introduced by A. Frabetti and developed in the line of work of R. Borcherds and E. Herscovich.

Towards a quantum theory: Laplace pairing

The framework I develop is at present classical. The longer-term goal is to derive a quantisation procedure via a Laplace pairing, in the spirit of the constructions of C. Brouder and A. Frabetti. The passage from classical to quantum along this route is not yet well understood in the equivariant setting, and I am interested in the obstructions that arise.

Categorical tools

The approach relies on several categorical structures: species (in the sense of Joyal), operads, and 2-monoidal structures in the line of R. Borcherds and E. Herscovich. As part of my current work, I am developing fibred versions of these structures, motivated by the needs of the equivariant setting.

Other interests and background

I have a working knowledge of orbifolds, in which I originally developed constructions related to my current research before reformulating them in the equivariant setting. The two perspectives are largely interchangeable, but the equivariant formulation has proved more practical for my purposes.

Work in progress

• Equivariant 2-Poisson Algebra Bundles over Configuration Spaces, in preparation. See the Publications page.

For exchanges on these topics, or if you work in related areas, please feel free to contact me.