I’m a mathematician.
Much of my work involves topics in Algebraic Geometry and related areas, such as number theory and computing.
I was a tutor at Brasenose College, Oxford and, before that, a lecturer at Cardiff University. I held post-doctoral positions at Bonn and Hannover (as a Riemann fellow). My PhD was completed at Bath under the supervision of Professor Gregory Sankaran. Aeons ago, I was a student at Lincoln College, Oxford.
Currently, I’m thinking about moduli spaces of compact hyperkaehler manifolds, their topology, and modular forms.
Research
General type results for moduli of deformation generalised Kummer varieties Produces general type results for moduli spaces of deformation generalised Kummer varieties; strengthening earlier results via new methods.
Orbits in lattices Introduces algorithms for calculating orbits of vectors in lattices and orbits of isotropic sublattices. Explains connections to computer arithmetic of automorphic forms for O(2,n) and compactifications of orthogonal modular varieties. Associated code can be found here.
The Baily-Borel compactification of a family of orthogonal modular varieties Studies the Baily-Borel compactification of orthogonal modular varieties related to moduli spaces of hyperkähler manifolds of deformation generalised Kummer type, with an emphasis on the classification of boundary components, incidence relations and associated combinatorics.
On the Kodaira dimension of the moduli of deformation generalised Kummer varieties Produces general type results for orthogonal modular varieties related to moduli spaces of hyperkähler manifolds of deformation generalised Kummer type. Makes use of automorphic forms techniques, toric geometry, toroidal compactifications and lattice theory.
Boundary combinatorics of orthogonal modular 4-folds Studies combinatorial problems related to the singularities and boundary components of toroidal compactifications of orthogonal modular varieties associated with the moduli of algebraic deformation generalised Kummer 4-folds.
Moduli of deformation generalised Kummer manifolds (PhD thesis, University of Bath) Studies lattice and combinatorial problems related to orthogonal modular varieties (and compactifications) associated with moduli spaces of deformation generalised Kummer varieties.
Teaching
I've taught various courses in Pure Mathematics, Applied Mathematics and Computing; ranging from group teaching in pairs, to lecturing to large audiences.
I’m a Fellow of the HEA and I occasionally write about teaching matters.
What are the pictures?
The graphs represent incidence relations between boundary components in the Baily-Borel compactification of orthogonal modular varieties. Sometimes they have a general combinatorial description; sometimes they don't, but can be calculated algorithmically using a computer. Why not have a look at my code on GitHub?
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