Dr Thomas Winyard

I study topological solitons, a beautiful class of objects which appear at every scale of the physical world, from cosmic strings stretching across the universe to the subatomic interactions of atomic nuclei. They arise in classical field theories where the dynamical field is twisted into a stable, knot-like configuration, providing a mathematically natural description of particle-like structures within continuous physical systems. Their stability arises from the underlying topology, and they appear as finite-energy solutions of nonlinear partial differential equations. Understanding the properties and interactions of these particle-like objects presents a fascinating challenge involving geometry, topology, analysis and numerical computation.
A central question is how solitons form, interact and move. When several solitons come together, they can form complex structures with surprising symmetries and rich dynamics. I use a combination of analytical and numerical techniques to find these solutions and explore the spaces of possible configurations. My recent research has focused on these interactions and dynamics in condensed matter systems, namely vortices in unconventional superconductors and magnetic skyrmions in chiral magnets. My research has helped show how the broken symmetries of these systems give rise to exotic solitons with unusual bound states and novel dynamical behaviour.

Specific areas of research include:

• topological solitons and nonlinear field theories
• skyrmions and the nuclear Skyrme model
• vortices and superconductivity
• multicomponent and unconventional superconductors
• fractional vortices and vortex lattices
• magnetic skyrmions and chiral magnets
• soliton dynamics and interactions
• numerical methods for nonlinear field theories

See my website for more recent academic developments in my research.