## Academic

### Bio

I graduated from Imperial College London with an MSci in Mathematics in August 2021. My final year research project was titled “An Introduction to Seiberg-Witten theory” and was supervised by Steven Sivek.

Since February 2022, I’ve been a PhD candidate 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 in the School of Mathematics.

A (slightly censored) copy of my CV dated 2023-01-26 can be found here. Please contact me for a full copy.

### Research interests

My broad research interests lie in Differential Geometry and Mathematical Physics with a particular focus on the application of gauge theory to problems in Kähler geometry and the study of vector bundles over complex algebraic curves.

#### Current research

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.

I’m currently studying a class of solitons which arise in the
Abelian Higgs model called *vortices*. The structure of
vortex moduli spaces is closely linked to the algebro-geometric
concept of a stable
vector bundle (see Bradlow
1990 and Bradlow
1989). I’m using this relationship to model the dynamics of
vortices in a certain parametric limit.

### Talks given

- “An Introduction to Vortices” at the University of Leeds School of Mathematics Pure PGR Seminar (Dec 2022)
- “Vortices near the Bradlow limit” at the University of Leeds School of Mathematics PGR Conference (Feb 2022) (slides)
- “Characteristic classes and (another) proof of the Hairy Ball theorem” at the Imperial College UG Colloquium (Feb 2021)
- “What we mean by the Lagrangian: Differential Geometry in Mechanics” at the Warwick Imperial Conference (Mar 2019)