Homotopical algebra and quantum field theory

Start date

1 October 2024


3.5 years

Application deadline

Funding source

UKRI and/or University of Surrey

Funding information

We are offering the UKRI standard stipend (currently £18,622 per year) with an additional bursary of £1,700 per year for full 3.5 years for exceptional candidates. In addition, a research, training and support grant of £3,000 over the project is also offered. Full home or overseas tuition fees (as applicable) will be covered.


Homotopy algebras have recently been identified to underpin any quantum field theory. In particular, they provide a powerful mathematical framework to analyse the mathematical structures of quantum field theory. 

• Part 1: Scattering amplitudes, the key quantities that are used to make contact between theory and experiment, are encoded in the higher products of homotopy algebras. This project aims at understanding scattering amplitude recursion relations through the lens of homotopy algebras. 

 • Part 2: Integrable quantum field theories are very particular theories in that they allow to be solved fully, at least in principle. Such theories feature prominently in the realm of gauge-gravity correspondences, notably the AdS/CFT correspondence. This project aims at analysing integrability through the lens of homotopy algebras.

Eligibility criteria

Open to both UK and international candidates.

Up to 30% of our UKRI-funded studentships can be awarded to candidates paying international rate fees. Find out more about eligibility.

You will need to meet the minimum entry requirements for our Mathematics PhD programme.

How to apply

Applications should be submitted via the Mathematics PhD programme page. In place of a research proposal, you should upload a document stating the title of the project that you wish to apply for and the name of the relevant supervisor.

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Application deadline

Contact details

Martin Wolf
25A AA 04
Telephone: +44 (0)1483 684770
E-mail: m.wolf@surrey.ac.uk

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