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.
The relation between algebraic and geometric structures in the context of integrable systems is a quickly developing subject, and my aim is to be part of this global investigation. At the moment, I am interested in the representation spaces of particular quiver algebras which are endowed with a Poisson bracket. 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 https://doi.org/10.1016/j.geomphys.2017.08.006. 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. Additional generalisations are in preparation.
Currently, we are looking at a way to derive elliptic versions of the past works.
Before my arrival in Leeds, I worked in the field of graded geometry, on which I wrote an introductory paper : https://link.springer.com/article/10.1007/s40879-017-0138-4 .
- BSc Physics
- BSc Mathematics
- MSc Mathematics