Profile
Biography
I did my undergraduate studies at the University of Cambridge where I also obtained my PhD in 2008. I held three postdoctoral positions at the ENS in Paris, at DESY in Hamburg and at the University of York. I then moved to be a Lecturer at the University of Hertfordshire from 2012 before becoming a Reader at the University of York in 2018
Research
Overview
My research interests lie in the theory of classical and quantum integrable systems, both finite and infinite dimensional. I am particularly interested in the problem of quantisation of classical integrable field theories in 1+1 dimensions. I am also interested in dualities between integrable systems, such as the AdS/CFT correspondence or the ODE/IM correspondence.
Research group(s)
Mathematical Physics and Quantum Information
Available PhD research projects
I am happy to supervise PhD projects in the general area of classical and quantum integrability, which can be tailored according to the student’s interests and preferences. Examples of possible topics for PhD projects are:
*Classical/quantum dualities:* Dualities in Mathematical Physics provide deep and usually unexpected connections between two seemingly different theories. Owing to their exact solvability, integrable systems provide perfect arenas for rigorously studying many examples of dualities. A well known example is the boson/fermion duality between the sine-Gordon model and the massive Thirring model, two quantum integrable field theories. Dualities also exist between classical and quantum integrable field theories, such as in the celebrated ODE/IM correspondence. Potential PhD projects would explore mathematical aspects of the ODE/IM correspondence through its connection with Gaudin models and the geometric Langlands correspondence.
*Higher-dimensional integrability:* Integrable field theories in 2-dimensions have been extensively studied and the underlying integrable structures at play are well understood. The latter were recently found to have a deep gauge theoretic origin in 4-dimensional semi-holomorphic Chern-Simons theory and an intimately related algebraic origin in the framework of affine Gaudin models. In stark contrast, integrable field theories in higher dimensions are much less developed and only very few examples are known. Potential PhD projects would explore higher-dimensional integrable structures using various higher-dimensional analogues of semi-holomorphic Chern-Simons theory and affine Gaudin model inspired techniques.
