Dr Vincent Caudrelier

Profile

I have an MSc from the French 'Grande Ecole' Supaero and an MSc from the University of Cambridge (DAMTP Part III of the Mathematical Tripos, with distinction), both obtained in 2002. I obtained a PhD in Theoretical Physics in 2005 from the Laboratoire d'Annecy-le-vieux de Physique Théorique, Université de Savoie, with distinction. I went on to do a post-doc at the Department of Mathematics, University of York, as an EPSRC research fellow. This led to my hiring at City University London in 2007. In 2016, I joined the School of Mathematics at the University of Leeds.

Responsibilities

• Integrable Systems seminar organiser
• Editor for Proceedings of the Royal Society A

Research interests

I am interested in the area of Mathematical Physics known as integrable systems. They appear in all sorts of areas: classical and quantum mechanics, classical and quantum field theory, statistical mechanics, and in various forms: models over discrete or continuous spacetime. They share common features that are encapsulated in rich and important mathematical structures like Poisson-Lie groups, for classical integrable (field) theories and quantum groups, for quantum integrable (field) theories. The most famous equation related to these structures is the Yang-Baxter equation (classical or quantum). 

A distinctive feaure of integrable systems is their high degree of symmetry which allows for exact calculations and explicit solutions for physically interesting quantities. For instance, correlation functions in quantum spin chains or long-time asymptotics of solutions of integrable PDEs can computed analytically and exactly. Typical domains of application are condensed matter physics,  theoretical physics, nonlinear waves dynamics in optics, fluid mechanics or plasma physics, 2D statistical models for percolation, etc.

One of my areas of focus is the study of the effect of boundaries and/or defects/impurities on the structure of these models and generalisations to more complicated graph structures. I have developed a scheme to formulate the inverse scattering method for integrable PDEs on (star) graphs. More recently, I have been concentrating on an emerging topic aiming at describing integrability purely within the Lagrangian formalism: Lagrangian multiforms theory. A strong motivation in the (near) future is to quantize integrable field theory using Feynman’s path integral and Lagrangian multiforms.

Professional memberships

• Editor for the Proceedings of the Royal Society A

Research groups and institutes

• Applied Mathematics

Current postgraduate researchers

• Matteo Stoppato
• Jacob Richardson
• Jean-Yves Desaules
• Anup Anand Singh

Projects

<li><a href="//phd.leeds.ac.uk/project/1168-quantisation-of-integrable-field-theories-and-lagrangian-multiform">Quantisation of integrable field theories and Lagrangian multiform</a></li>