Research Interests:
 Topological Solitons
Topological solitons are stable, finite energy, particlelike 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.
Wiki
arXiv

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.
Wiki
arXiv

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 GinzbergLandau equations. When extended to the full 3d model they represent vortex strings of magnetic flux through a superconducting sample. In particular I have an interest in multicomponenet systems that lead to interesting vortex interactions and has generate 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.
Wiki
arXiv

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

Academia:
Publications:

Scattering of broken baby Skyrmions.

Conferences and Talks:
 (22/11/17)  South East Mathematical Physics Seminar  Vorticies in Multicomponent Superconductors  [Slides]
 (17/11/17)  Leeds University Integrable Systems Seminar  Vorticies in Anisotropic Multicomponent GinzburgLandau 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 Multicomponent 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.
 (19/12/11)  YTF Conference 2011  Conference page here.
Teaching:
Topological Solitons (graduate)
Old Resources:
Linear Algebra
Analysis
Transitions
Less Academic Interests
Durham University Freefall Club  BCPA 


