Gautam Chaudhuri / About



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