I am working at the intersection of algebra, mathematical physics and mathematical biology. I am interested in aspects of geometry and symmetry wherever they occur in the natural world. Concrete applications in three dimensions include the structure of viruses, fullerenes and quasicrystals; less intuitive perhaps, but intimately mathematically related, are the geometry of higher dimensions (in particular that of four and eight dimensions and ADE correspondences), and applications to gravitational and high energy physics, such as string theory and the structure of cosmological singularities.
I am interested in various aspects of euclidean, spherical, hyperbolic and conformal geometry. Interesting symmetries seem to revolve around reflections and rotations - related concepts are Coxeter groups, root systems, Lie algebras and Lie groups, lattices and quasilattices. Clifford algebra is a particularly convenient framework for reflections and I have shown that it can thus be a useful tool for topics in geometry and symmetry.
I have had a long-standing interest in immunology and virology of nearly 20 years, having done a placement at the Institute of Immunology and my national service at the Institute of Virology, Essen. The obvious connection with the above mathematics is via the highly symmetric structures of virus capsids. But I am also interested in virology more broadly, in particular immunological, clinical, ecological and evolutionary aspects, and recently also applications of machine learning in this context.
I am passionate about science outreach (I have coordinated the international Pint of Science Festival in York twice, was twice Chapter manager for York, Hull and Bournemouth, and am now Chapter manager for York, Hull and Leeds) and diversity (I have been a panelist for the Equality Challenge Unit's Athena SWAN and Race Equality Chartermarks and am a member of the York St John self-assessment team (SAT)).
I am a senior lecturer in mathematical sciences at York St John University, where I am developing degrees in Mathematics and Data Science, as well as a Data Science Degree Apprenticeship. These cutting-edge degrees straddle pure and applied aspects, and have interdisciplinarity, communication, digital literacy and employability at their heart.
I was previously a lecturer in Mathematics and Biology at the University of York (teaching Applications of Group Theory in Virology, Principles of Molecular Virology, Numerical Techniques for Modelling Biological Systems, Vector Calculus and Science Communication) and in Mathematics at the University of Durham (teaching Single Maths A, Mathematical Physics and Mathematics for Scientists and Engineers). Previous and current institutional affiliations include York Maths, York Biology, York Cross-disciplinary Centre for Systems Analysis (YCCSA), Durham Maths, ASU Physics, Durham Physics, Cambridge Maths and Physics, Kavli Institute for Cosmology Cambridge, Institute of Virology Essen and Harvard.