Department of Pure Mathematics

Thomas Winyard
Postdoctoral Researcher
University of Leeds
Office: 9.30

Thomas Winyard

Research Interests:

  • Topological Solitons
  • Topological solitons are stable, finite energy, particle-like solutions of nonlinear wave equations. They arise in a variety of applications in several areas including particle physics, cosmology and condensed matter physics. Here are some examples of 3D topological solitons in which I am interested.

    A 32 hyperbolic Skyrmion configuration.
    A plot of a charge 32 Skyrmion configuration in hyperbolic space.
  • Skyrmions/Planar Skyrmions
  • Skyrmions are interesting both from a mathematical point of view and as a powerful candidate for a solitonic description of nuclei, where the number of solitons is equivalent to the baryon number. The Skyrme model is a 3d field theory and has a 2d analogue in the form of planar skyrmions. There are also many different topological solitons (e.g. monopoles and instantons) which can be related to the Skyrme model. Moreover, many different techniques can be applied to this model. One way is to solve the equations numerically with the help of a large computer. However, often more insight is gained by using approximations.
    A 17 Instanton Configuration.
    Plot demonstrating the interesting symmetries of the Skyrmion solutions for increasing charge.
  • Vorticies
  • Vorticies are topological solitons in a two dimensional gauge theory that appear in superconducting systems through the Ginzberg-Landau equations. When extended to the full 3d model they represent vortex strings of magnetic flux through a superconducting sample. In particular I am interested in multi-componenet systems that lead to interesting vortex interactions and have generated a large amount of interest in both theoretical and experimental physics. There are also interesting results in considering vorticies on other Riemannian surfaces, this can make the moduli space more tractable than the flat plane case.

    Magnetisation of a multicomponenet superconductor.
    Contour plot of vorticies forming due to the magnetisation of a superconductor in an external magnetic field.



Scattering of broken baby Skyrmions.
Scattering of broken baby Skyrmions.

Conferences and Talks:

  • (23/03/22) - SMSAS Sustainability Lecture - Solitons: how studying Tsunamis lead to levitation - [Slides]
  • (25/02/22) - Kent mathematical physics seminar - Constructing Skyrmions from instantons (board talk)
  • (30/06/21) - Solitons and (non)-integrability in Geometry (SIG) - Skyrmion from instantons - [Slides]
  • (21/06/21) - Condensed Matter and Quantum Materials (CMQM) - Non-London behaviour in nematic Ginzburg-Landau and experimental signatures [Poster]
  • (09/01/20) - Frontiers in Condensed Matter (Bristol) - Magnetic Signatures of Domain Walls in s+is and s+id Superconductors - [Slides]
  • (28/09/19) - Nordita Condensed Matter Seminar - Length Scales in Anisotropic Superconductors (Board Talk)
  • (15/09/19) - KTH Theoretical Physics Seminar - Skyrmions in Frustrated Ferromagnets Below Critical External Field - [Slides]
  • (23/08/18) - Alba Nova Mathematical Physics Seminar - Anisotropy in Ginzburg Landau Theories - [Slides]
  • (02/07/18) - Low Energy Effective Dynamics of Skyrmions (LEEDS) - The Effects of Anisotropy in Multicomponent Vortex Models - [Slides]
  • (18/06/18) - Solitons and (non)-integrability in Geometry (SIG) - Solitons and anisotropy- [Slides]
  • (22/11/17) - South East Mathematical Physics Seminar - Vorticies in Multicomponent Superconductors - [Slides]
  • (17/11/17) - Leeds University Integrable Systems Seminar - Vorticies in Anisotropic Multi-component Ginzburg-Landau theory and the Dichotomy of Superconductor Type - [Slides]
  • (14/11/16) - Alba Nova Mathematical Physics Seminar - The Skyrme Model and recent advancements (Board Talk)
  • (13/09/16) - 2nd Geometrc Models of Nuclear Matter Conference - Anisotropic Multi-component Superconductors - Conference page here
  • (21/02/16) - KTH condensed matter Seminar - Numerical Solutions to the Skyrme Model in (2+1) and (3+1) and their Formation - [Slides]
  • (21/10/15) - University of Leeds Geometry Seminar - Baby Skyrmions and Skyrmions in AdS - [Slides]
  • (26/06/15) - University of Kent Mathematical Physics Seminar - Baby Skyrmions in AdS and Extensions to (3+1) Dimensions - [Slides]
  • (22/06/15) - Durham CPT Student Seminar - Massless baby Skyrmions in AdS_3 and extensions to 3+1 dimensions [Slides]
  • (20/08/14) - Geometric Models of Nuclear Matter - Hyperbolic Skyrmions - Conference page here - [Slides]
  • (28/07/14) - 1st Early Career South East Mathematical Physics Seminar - Skyrmions in hyperbolic space - Conference page here - [Slides]
  • (19/12/13) - YTF Conference 2013 - Instantons, monopoles and Skyrmions in hyperbolic space - Conference page here - [Slides]
  • (15/05/13) - North British Mathematical Physics Seminar 38 - Broken Baby Skyrmions - Conference page here - [Slides] - [Video1] [Video2]
  • (20/02/13) - Durham Topological Solitons Seminar - Broken Baby Skyrmions - [Slides] - [Video1] [Video2]
  • (18/02/13) - Durham CPT Student Seminar - Broken Planar Skyrmions - [Slides] - [Video1] [Video2]
  • (18/12/12) - YTF Conference 2012 - Conference page here.
  • (02/09/12) - BUSSTEPP 2012 - Conference page here.


MATH1060 Introductory Linear Algebra

Old Resources:

Topological Solitons (graduate)
Linear Algebra

Less Academic Interests

Durham University Freefall ClubBCPA