Geometry and dynamics of topological solitons

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