EPSRC DLA studentship - Categorically tweaking vertex operator algebras

Symmetries in Nature help us to understand its most fundamental laws. A simple example is rotational symmetry, invariance of a phenomenon if we observe it independently of the viewing angle. The more uncommon a symmetry is, the more exotic and original the mathematical structures needed to describe it. In recent decades, there has been a substantial effort to understand the structures related to conformal symmetry, a particularly rare symmetry which preserves angles (but not for example sizes). This has created an active, rich, and cutting-edge field of world-wide research.  

Two examples of these structures related to conformal symmetry are vertex operator algebras and modular tensor categories. The study and classification of these two seemingly very different, but closely related structures, have historically followed different paths, and several questions remain for the completion of their respective classifications. This project will combine the existing knowledge on each side to provide a fresh view on both classifications, importing results and techniques from one side to the other, and advancing our knowledge of these structures and their generalizations.  

Framed within the UKRI Responsible Research and Innovation, the abstract nature of the project seeks the highest benefit and impact in quantum algebra. However, they have a strong potential to produce fin-tech innovations: modular tensor categories could also have applications in quantum information and computing, while the number-theoretical aspects of this work could have remarkably interesting applications to cryptography and could be crucial to secure data and promote innovation and infrastructure development. Further, some of the algebraic structures involved in the project are related to topics in the research forefront of statistical mechanics and could help to produce more renewable energy and reduce the carbon footprint, aligning to sustainable manufacturing and low-carbon energy. 

What we offer:

Cardiff's School of Mathematics provides an excellent postgraduate research environment including:

·    research facilities at Abacws (co-designed by our PGR community),

·    a vibrant research culture including a wide range of research events,

·    access to national course centres in mathematics, statistics and Operational Research,

·    comprehensive professional skills training offered by Cardiff’s Doctoral Academy.

·  collaborations with other disciplines and with a wide range of external partners (industry and society).

The PGR community is very active in running the SIAM-IMA Student Chapter, a valuable forum for exchange of ideas and public engagement.

This studentship will be undertaken within the Geometry, Algebra, Mathematical Physics and Topology (GAPT) research group at the School of Mathematics. The group’s members have wide-ranging interests, and offer a dynamic environment for the student to engage with experts in operator algebras and many other fields in mathematics and other disciplines. The group hosts a weekly seminar inviting external speakers.

Completing a PhD in mathematics opens up a range of possible next steps, from continuing an academic career to working in mathematically technical roles in industry.

The 3.5 year studentship includes fees, stipend at the UKRI rate and a Research Training Support Grant to cover costs such as research consumables, training, conferences and travel.

The start date for this PhD studentship is 1 October 2025.

What you bring:

You should have a 1st or upper 2nd class UK Honours degree (or equivalent) and/or a Master’s degree in mathematics or a suitable related subject.

Applicants for whom English is not their first language must demonstrate their proficiency by obtaining an IELTS score of at least 6.5 overall, with a minimum of 5.5 in each skills component, or equivalent qualification.

Shortlisted candidates will be invited to attend an interview.

Cardiff University is committed to supporting and promoting equality and diversity and to creating an inclusive research environment. We particularly welcome applications from underrepresented groups.

How to apply:

Applicants should apply through the Cardiff University online PhD application portal, for a Doctor of Philosophy in Mathematics with an entry point of 1 October 2025.

In addition to the standard application form, applicants should also:

* Attach a CV. Guidance on CVs for a PhD position can be found on the FindAPhD website .

* Ensure your personal statement (as part of the university application form, or as a separate attachment, if you prefer) provides a clear explanation of your research interest, preparation undertaken, and an understanding of the project.

Your personal statement should be no more than 500 words, and address the following questions:

1. What are your scientific research interests and ambition?

2. How has your academic and/or professional journey prepared you for PhD study? (for instance, give examples of work you particularly enjoyed, of challenges you overcame, of connecting with others about your work or ideas, of showing inventiveness, of developing new skills and knowledge)

3. Why do you think this project is important?

Incomplete applications will not be considered.

For general information about EPSRC-funded studentships at Cardiff, please see EPSRC - Study - Cardiff University .

Please note that the 'register interest' option will not submit an application. Please follow the instructions above and submit your application via our online portal.