About the Project
A fully funded PhD opportunity to participate in the world-leading research undertaken by the EPSRC Doctoral Landscape Award at the University of Sheffield.
Supervised by Dr Cheuk Yu Mak and Prof Evgeny Shinder.
The University of Sheffield is one of the leading Russell Group universities in the UK. We carry out cutting-edge research with strong links to industry. When you enrol to do a PhD with us, you will be working with world-leading academics and have access to top of the range facilities. As a PhD student you will have the opportunity to gain skills not only to conduct research, but also to take your career to the next level, whether you want to stay in academia, go into industry or the public sector, or set up your own company. You will have access to a range of training and support services to help you excel in your studies and beyond.
Project Description
This project explores exciting new directions in modern geometry, where ideas from topology, algebra, representation theory and mathematical physics come together. The central theme is symplectic geometry, a field that studies geometric spaces with structures arising naturally from classical mechanics and that has become a fundamental language across many areas of modern mathematics and theoretical physics.
The aim of this project is to develop new mathematical ideas and techniques for understanding the deep relationships between geometry, topology and algebra. A central question is how geometric spaces can encode rich algebraic and topological information, and how these structures can be used to uncover new connections between different areas of mathematics.
The project will involve the development and application of modern tools such as Floer theory, symplectic invariants, mirror symmetry and categorical methods. These techniques allow mathematicians to study complicated geometric objects by associating them with algebraic structures that capture essential information about their shape and behaviour.
Possible research directions include the study of symplectic manifolds and their invariants, the construction and application of Fukaya categories, connections between geometry and representation theory, and interactions with ideas from quantum field theory and mathematical physics. These directions aim to reveal common principles underlying structures that have traditionally been studied from different perspectives.
The project is motivated by fundamental questions about the unity of mathematics: how different mathematical objects and theories are connected, and how geometric ideas can provide new insights into topology, algebra and physics. By developing new methods and establishing unexpected connections, the project aims to contribute to the future development of modern geometry and its applications across mathematics.
Students involved in this project will have the opportunity to learn advanced techniques in geometry and topology, work on challenging problems at the forefront of current research, and engage with a broad range of ideas spanning pure mathematics and mathematical physics. The project provides an environment for developing the skills needed to pursue research in modern mathematics and to contribute to new discoveries in this rapidly developing field.
How to apply
Interested candidates are strongly encouraged to contact the project supervisors to discuss your interest in and suitability for the project prior to submitting your application.
Please refer to the EPSRC DLA webpage for detailed information about the EPSRC DLA and how to apply.
Applicants must ensure that they use the correct application form linked to the EPSRC DLA webpage and must submit an application for October 2027 entry. The form is unique to the EPSRC DLA. It contains the list of advertised projects from which to select, and three questions specific to the DLA.
The application deadline is 17:00 GMT 13 January 2027.
The majority of our DLA studentships will be allocated to candidates who qualify for Home fee status, in accordance with EPSRC funding regulations which place strict limits on international recruitment.
Funding Notes
The award will fund the full tuition fee and a maintenance stipend at the UKRI rate (currently £21,805 per annum) for 3.5 years, as well as a research grant to support costs associated with the project.
