Since February 2022, I’ve been a PhD candidate in the School of Mathematics at the University of Leeds researching the Geometry and Dynamics of Topological Solitons. I’m studying under the supervision of Martin Speight and Derek Harland as a part of the geometry group.
A (slightly censored) copy of my CV (dated ) can be found here. Please contact me for a full copy. For a list of my written work and talks/posters presented (with links), please see my works page.
Research interests
My broad research interests lie in Differential Geometry and Mathematical Physics with a narrower focus on the application of gauge theory to problems in Kähler geometry and the study of vector bundles over complex algebraic curves.
Click here for a detailed description of my PhD topic.
The main objects of study in my PhD are (topological) solitons. Solitons are certain configurations of physical fields (e.g. electric and magnetic fields) which exhibit particle like behaviours. In particular solitons are local objects with their field strengths decaying as one moves away from a soliton “core”. Mathematically, this is modelled as a section of some fibre bundle along with a connection which together minimise some energy functional.
Topological solitons are those which cannot decay into the vacuum state because they exhibit some sort of winding behaviour, similar to how a string wound round a vertical pole cannot be pulled straight. Associated to a topological soliton is an integral topological charge which is preserved as the soliton evolves in time, in the string analogy this is akin to the number of times the string is wound around the pole.Current research
I’m currently studying a class of solitons which arise in the Abelian Higgs model called vortices. The dynamics of vortices is well approximated by geodesic motion on an associated moduli space, and I am attempting to understand this motion in certain parametric limits.
Concretely, I am trying to understand geodesic motion in the dissolving limit, where the Higgs field of the vortex vanishes; and as the vortex charge increases.