People

Dr Josh Cork

Teaching Fellow in Mathematics

School/Department: Computing and Mathematical Sciences, School of

Email: jc893@leicester.ac.uk

Web: Personal webpage

Profile

I am a mathematician and mathematical physicist. I completed my Ph.D. between 2014 and 2018 at the University of Leeds. Before coming to Leicester I was a Teaching Associate in Pure Mathematics at Lancaster University and a Postdoctoral Research Assistant in the Institut für Theoretische Physik at Leibniz University Hannover Germany.

I hold associate fellowship of Advance HE, the national body for teaching in Higher Education in the UK.

Research

My research is mainly focused on gauge theory and topological solitons. Topological solitons are, loosely speaking, stable solutions to classical field equations which owe their stability to global (topological) properties of the fields, for example a winding number. Solitons play a key role in physics as they are candidates for particles in the theory. Important examples (which I am interested in) are instantons in Yang-Mills theory, monopoles in Yang-Mills-Higgs theory, and skyrmions in the Skyrme model (a geometric model of nuclei).

The majority of my research has been devoted to developing and improving tools for constructing exact and approximate examples, and classifying solitons. For example, I have constructed and classified calorons (periodic instantons) with cyclic symmetries, and recently I have been working (along with my collaborators) on how to extract information about low-energy properties of nuclei in the three-dimensional Skyrme model via instantons and calorons in four-dimensions.

There is a global community who are actively involved in studying topological solitons. Find out more via the lively online solitons at work network.

Publications

J. Cork and C. Halcrow (2022) ADHM skyrmions. Nonlinearity, 35 , pp. 3944. DOI: https://doi.org/10.1088/1361-6544/ac72e6

J. Cork, D. Harland, T. Winyard (2021) A model for gauged skyrmions with low binding energies. Journal of Physics A: Mathematical and Theoretical, 55 , pp. 015204. DOI: https://doi.org/10.1088/1751-8121/ac3c81

J. Cork, E. S. Kutluk, O. Lechtenfeld, A. D. Popov (2021) A low energy limit of Yang-Mills theory on de Sitter space. Journal of High Energy Physics, 89 . DOI: https://doi.org/10.1007/JHEP09(2021)089

J. Cork (2018) Skyrmions from calorons. Journal of High Energy Physics, 11 . DOI: https://doi.org/10.1007/JHEP11(2018)137

J. Cork (2018) Symmetric calorons and the rotation map. Journal of Mathematical Physics, 59 . DOI: https://doi.org/10.1063/1.5017193

Supervision

I currently supervise one PhD student, Matthew Dales

Please contact me if you are interested in working with me on a postgraduate degree. Potential (broad) project topics include: Constructions of instantons; quantisation of skyrmions; geometry of topological solitons.

I also offer 3rd and 4th year undergraduate research projects. The projects offered are listed by year below.

2022-23: The geometric topology of knots and links (Year 3)

Teaching

Semester 1:

MA3152 & MA4152 Curves and Surfaces

MA3516 Mathematics Research Project


Semester 2:

MA1027 Plane Geometry

MA2021 Differential Equations and Dynamics

MA3516 Mathematics Research Project

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