Dr Josh Cork

Teaching Fellow in Mathematics

School/Department: Computing and Mathematic Sciences, School of


Web: Personal webpage


I am a 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.


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.


J. Cork and C. Halcrow (2022) ADHM skyrmions. Nonlinearity, 35 , pp. 3944. DOI:

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:

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:

J. Cork (2018) Skyrmions from calorons. Journal of High Energy Physics, 11 . DOI:

J. Cork (2018) Symmetric calorons and the rotation map. Journal of Mathematical Physics, 59 . DOI:


I do not currently supervise any students.

Potential (broad) project topics include: Constructions of instantons; quantisation of skyrmions; Geometry of topological solitons.


Semester 1:

MA3152 & MA4152 Curves and Surfaces

Semester 2:

MA1027 Plane Geometry

MA2021 Differential Equations and Dynamics

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