Josh Cork

Josh Cork

Profile

I am an MMath graduate from Durham University, and have recently completed my PhD at the University of Leeds under the supervision of Derek Harland. I was awarded a Graduate Teaching Assistantship for my PhD funding.

Research interests

Broadly, my research interests incline towards understanding various aspects of pure mathematics found in physics. In particular, I am interested in physical systems with topological and differential geometric structure. Various physical field theories possess topological soliton configurations -- particle-like solutions to equations of motion which are stable under continuous deformations. Two prominent examples are the Yang-Mills, and Yang-Mills-Higgs gauge theories, whose topological solitons are generally called instantons and monopoles respectively. Both instantons and monopoles have a rich geometry, providing examples of hyperkaehler manifolds, and links to geometric invariant theories, alongside important physical interpretations. My current research has focused on instantons for which one direction is periodic; these are also known as calorons. Alongside many fascinating mathematical properties, calorons play an interesting role in physics, especially in lattice gauge theories, and have been linked to the problem of confinement. Calorons are also explicitly related to the aforementioned topological solitons, but are significantly less well-understood. Another field theory with topological soliton solutions is the Skyrme model, which is related to nuclear physics, and its solitons are known as skyrmions. Instantons, monopoles, and skyrmions, have long been known to be related to each other in one way or another, and some of these relationships are not so well-understood. Recently I have developed a way to relate calorons to skyrmions, and am interested in its implications on the wider relationships between instantons, monopoles, and skyrmions.