Maxime Fairon

Maxime Fairon

Profile

I am a PhD student in integrable systems and geometry supported by a University of Leeds 110 Anniversary Research Scholarship

Before joining Leeds, I studied at the Université Catholique de Louvain in Belgium, where I was awarded (the degree equivalent to) a MSc in Mathematics, after having completed a BSc in Mathematics and a BSc in Physics at the same institution.

Research interests

The relation between algebraic and geometric structures in the context of integrable systems is an extremely rich subject, and my aim is to be part of this global investigation. At the moment, I am interested in the representation spaces of algebras associated to particular quivers, and how to understand the Poisson structure of these spaces within the algebras themselves. My goal is to examine such structures in order to find new integrable non-linear differential equations and study their solutions. Potential applications could exist in a variety of subjects, such as quantum algebras, statistical mechanics or string theory.

The first results obtained while working on this project can be found as this article. Some multiplicative quiver varieties defined from a cyclic quiver are studied, and their link to the Ruijsenaars-Schneider (RS) model and some variants is explained. This is joint work with my supervisor, Oleg Chalykh.

We investigated spin generalisations of this work, and we are able to prove a conjecture describing the form of the Poisson bracket for the spin trigonometric RS model in this paper. I looked at the analogous models for cyclic quivers here, while additional generalisations will be developed in my thesis.

Currently, we are looking at a way to derive elliptic versions of the past works, and understand their relation to integrable hierarchies.

Before my arrival in Leeds, I worked in the field of graded geometry, on which I wrote an introductory paper .

Qualifications

  • BSc Physics
  • BSc Mathematics
  • MSc Mathematics