Geometry and dynamics of topological solitons

Supervisor(s)

Contact Professor Martin Speight or Dr Derek Harland to discuss this project further informally. 

Project description

Field theory is the natural mathematical language to explain fundamental physics, from particle physics, to condensed matter, to gravitation and cosmology. In many field theories it is possible for the dynamical field, a map from spacetime into some manifold, to wrap itself up rather like a high-dimensional knot. Such a field traps large amounts of energy in a smooth, spatially localized lump, called a topological soliton, which can move around and interact with other solitons in remarkably particle-like fashion. Solitons are natural candidates for fundamental particles (e.g. magnetic monopoles, protons, neutrons), but they also model large scale structures in condensed matter physics (e.g. vortices in superconductors) and cosmology (e.g. cosmic strings). There is a beautiful geometric theory of the dynamics of solitons which describes their motion in terms of the moduli space of static multisolitons, a mathematically rich and fascinating object in its own right.

The aim of this project is to study the geometry of topological solitons and connect it to their dynamics, in one of many possible specific contexts. There is flexibility to give the project an algebraic-geometric (e.g. twistor constructions in gauge theory) or differential-geometric flavour (e.g. geometry of the moduli space of harmonic maps), or even a more direct physical slant, with some numerical work (e.g. solitons in exotic superconductors or the Skyrme model of nuclear physics).

The Algebra, Geometry and Integrable Systems (AGIS) research group: The successful applicant will join a large and exceptionally vibrant research group, consisting of 14 permanent academic staff, 7 postdocs and over 15 students. The group runs 4 regular seminar series and is a node in 4 regional research networks. All members of the group are internationally recognized experts in their field, sought after as speakers at international research workshops and conferences, and several have been honoured with the award of fellowships or prizes. The group is an active participant in the MAGIC consortium, which provides specialist lecture courses for mathematics postgraduates at a network of Universities.

Entry requirements

Applicants should have, or expect to obtain, a first class honours degree in Mathematics or a related discipline (such as Theoretical Physics), or equivalent.

If English is not your first language, you must provide evidence that you meet the University’s minimum English Language requirements.

How to apply

Formal applications for research degree study should be made online through the university's website. Please state clearly in the research information section that the PhD you wish to be considered for is 'Geometry and dynamics of topological solitons’ as well as Professor Martin Speight as your proposed supervisor.

We welcome scholarship applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates.  All scholarships will be awarded on the basis of merit.

If you require any further information please contact the Graduate School Office, e: maps.pgr.admissions@leeds.ac.uk