4 Year GTA - The geometry of nuclei: skyrmions, holography, and gravitational instantons

About the Project

Open to UK Applicants only

Mathematics are offering 3 fully-funded Graduate Teaching Assistant (GTA) PhD studentships available for UK applicants, starting in September 2026.

Graduate Teaching Assistantships allow research students to fund their PhD through part-time teaching work with the University.

A Graduate Teaching Assistant is responsible to the Head of School and is expected to undertake teaching or other duties within the School - not normally exceeding 8-10 contact hours per week - while undertaking research leading to a PhD.

Approximately 80% of their time will be spent on their doctoral research and 20% on their GTA responsibilities. Training is provided to help Graduate Teaching Assistants develop their teaching related skills and enhance their professional competencies.

Project highights

• Developing rigorous geometric models of matter and fundamental interactions
• Establishing new links between solutions of integrable systems and physically important theories
• Exploring the geometry of curved spacetimes and the holographic structure of nuclear matter

Project description

The Skyrme model is a geometric model of nuclei. It has topologically-stable finite-energy solutions called skyrmions which model baryons. The field equations cannot be solved explicitly, prompting development of analytic approximations to complement expensive numerical computations and allow quantum treatments. Atiyah-Manton [1] proposed a surprisingly accurate approximation using self-dual Yang-Mills fields. Sutcliffe later explained its accuracy [2], demonstrating how the Skyrme model arises as a “holographic” dimensional reduction of Yang-Mills theory. Recent extensions to periodic Yang-Mills [3,4] have yielded gauged skyrmions, modelling fundamental interactions between nuclei. The Atiyah-Manton-Sutcliffe framework is the foundation of an active international programme aiming to probe analytic and qualitative properties of skyrmions using Yang-Mills fields.

This project will extend the Atiyah-Manton-Sutcliffe framework to gravitational instantons: 4D Riemannian solutions of Einstein’s equations with localised curvature properties. While ad-hoc attempts to obtain skyrmions from these exist [5], the systematic field-theoretic relationship remains unexplored. You will derive new Skyrme models corresponding holographically to Yang-Mills theory on gravitational instantons, comparing their solutions with the corresponding self-dual Yang-Mills fields. There is scope to focus on either phenomenological application, e.g., comparing with real nuclei and making links with QCD, structural properties, e.g., involving fiber bundle geometry and equivariant cohomology [6], or performing numerical simulations.

The project will suit students interested in the intersection of geometry, topology, and physics. It requires a diverse mathematical toolkit including differential geometry, PDEs, integrable systems, and gauge theory, and offers a route to high-impact publications in leading mathematical physics journals.

Project enquiries to Dr Josh Cork josh.cork@leicester.ac.uk

Application enquiries to pgrapply@le.ac.uk

To apply please refer to the application advice and use the application link athttps://le.ac.uk/study/research-degrees/funded-opportunities/maths-gta

Start 21 September 2026

Funding Notes

The 4 year GTA funded studentships provide:

• A combined teaching and stipend payment, currently. for 2026/7 this will be £21,805 per year, paid in monthly instalments
• Tuition fees at UK rates

References

[1] Atiyah & Manton (1989) Phys. Lett. B 222:438.
[2] Sutcliffe (2010) JHEP 2010:19.
[3] Cork (2018) JHEP 2018:43.
[4] Cork, Harland & Winyard (2022) J. Phys. A 55:015204.
[5] Dunajski (2013) Proc. R. Soc. A 469:20120576.
[6] Cork & Harland (2023) SIGMA 19:071.