Dr Maxime Fairon

Published: 19 February 2020

Integrable systems, mathematical physics, non-commutative Poisson geometry

Dr Maxime Fairon

School of Mathematics & Statistics

Type of fellowship Rankin-Sneddon Research Fellowship

Area of research  Integrable systems, mathematical physics, non-commutative Poisson geometry

Why did you choose to pursue a fellowship in your research career?

A few months before submitting my PhD thesis at the University of Leeds, I began to look at the possible next steps in my academic career. Since I had been developing a new point of view to tackle problems arising in mathematical physics at that time, it quickly appeared to be a better opportunity for me to investigate new connections between my work and other topics within my field, rather than applying for postdoctoral positions where I would work on other people’s projects which may not be related to what I was doing. Therefore, I began to state problems that I would be interested to know how to solve, and I was hoping that these questions would form the beginning of a research programme on which I would be working independently. This strategy turned out to be successful, and I am glad to say that I am currently investigating some of these problems as part of my fellowship.

Why work at the University of Glasgow?

Within the School of Mathematics and Statistics in Glasgow, there are research groups focusing on algebra, geometry and mathematical physics. As my research interests lie at the intersection of these three subjects, Glasgow is one of the most suitable places which can offer me a stimulating environment to carry on my works in progress and to collaborate with new people. 

How would you describe your research in 20 words or less?

Understanding physical systems of interacting particles using the representation theory of non-commutative algebras

What is your research highlight?

In November 2018, I posted a preprint on arXiv (the repository of preprints in mathematics & physics) which answered a conjecture made 20 years earlier about the Hamiltonian formulation of a particular system of interacting particles. A key aspect of that work which I did with my PhD supervisor is that we obtained this result by using a new range of techniques from a different field; we understood a geometric problem of interest to mathematical physicists by studying non-commutative algebras.  

What do you look for in a collaboration?

For me, a fruitful collaboration requires a small group of researchers with a common interest but different backgrounds. In that way, each collaborator can suggest ideas to pursue or techniques to use, and the others learn something from this new point of view.

How do you see your research impacting society?

The interesting aspect of mathematics is that you never know in advance where your research could be impactful. In my particular area, there exists a relationship between systems of interacting particles and solutions of equations governing wave phenomena, which are models used for example in hydrodynamics or optics, but which also appear in chemistry and biology. So, I would be glad to discover that, one day, my research was also used to understand models that appear in other fields, and that may be of direct interest to society as a whole.

What next?

At the moment, I am enjoying the fact that a fellowship allows to spend time to do research without worrying about finding another position on a short-term basis. I hope that I will be able to secure either a further fellowship or a position as a lecturer within 3 years, and that I will be tackling a more elaborate research agenda by that time.


First published: 19 February 2020