We invite applications to research degree programmes throughout the year. However, there are application deadlines for funded and self-funded PhDs starting in October, February and June. We suggest prospective students apply by 20 January 2025 for studies commencing in October 2025.
We welcome applications in any research area of interest to the Department. Prospective students are also encouraged to explore potential supervisors.
We welcome applications from self-funded students, who will receive a research training and support grant for conferences and research-related spend.
For funded opportunities please consult our ‘Funding’ tab for full details. Alternatively, candidates can apply for funded projects with the full list available in the ‘Explore our PhD Projects’ tab.
We welcome applications from all applicants and, in particular, those underrepresented in STEM subjects and academia.
Eligibility
- Applicants should hold, or expect to gain, a first or upper second-class degree in mathematics or a relevant related subject, and be exceptionally motivated for research.
There are a number of funding opportunities available. Some cover both stipend (to cover living costs) and tuition fees, while others may cover fees only.
All our PhD students, including those who are self-funded, receive a Research and Training Support Grant per annum to support training, attending conferences and research-related costs.
All scholarships, bursaries or other awards are offered on a competitive basis. Some funding opportunities may have earlier deadlines, so please check carefully.
The Department offers a range of funded PhD projects through a variety of funders, and research grants – set out in the next tab and searchable in King’s funding database.
- EPSRC Doctoral Landscape Award Studentships
Candidates who are accepted onto a research degree programme will be considered for Engineering & Physical Sciences Research Council (EPSRC) funding via our Doctoral Landscape Awards.
All eligible PhD applicants are considered for these awards when they apply to the Department. Please cite the code EPSRC-Maths-2025-26 in the Funding section of the application form. Please select option 5 ‘I am applying for a funding award or scholarship administered by King’s College London’ and type the code into the ‘Award Scheme Code or Name’ box. Please copy and paste the code exactly.
- Science & Technology Facilities Council (STFC)
Applicants for the Applied Mathematics Research: Theoretical Physics MPhil/PhD are eligible to apply for STFC studentship funding. Please cite the code STFC-Maths-2025-26 in the Funding section of the application form. Please select option 5 ‘I am applying for a funding award or scholarship administered by King’s College London’ and type the code into the ‘Award Scheme Code or Name’ box. Please copy and paste the code exactly. Find out more here.
The Martingale Foundation awards fully funded Scholarships for postgraduate degrees in the mathematical sciences at research universities, including right here at King's. Tuition fees and research expenses are fully covered, and Scholars receive a tax-free living wage stipend. Martingale Scholars also receive access to leadership and career develop through a multi-year programme of training and support. Find out more here.
The Heilbronn Institute for Mathematical Research (HIMR) is a partnership between UK government and the UK mathematics research community. The Institute funds a select number of PhD studentships per annum at King’s College London covering tuition fees, stipend and a research and training support grant. Find out more here.
There are also funded opportunities through our Centres for Doctoral Training:
An innovative PhD programme that cuts across the Health Faculties and the Faculty of Natural, Mathematical & Engineering Sciences. The programme offers postgraduate researchers fully funded positions with the aim of training the next generation of leaders in healthcare technology to improve healthcare systems using the cutting-edge framework of Digital Twins. Find out more here. Projects will be advertise early November.
A cross disciplinary CDT based in the Faculty of Dentistry, Oral & Craniofacial Science offers support for 3.5 years including a stipend at the current UKRI rate, home rate tuition fees, research expenses and support for training and career enhancement. Find out more and apply here.
King’s Quantum Centre for Doctoral Training brings together quantum practitioners in the Faculty of Natural, Mathematical and Engineering Sciences (NMES) with our world-leading quantum adopters - researchers deploying quantum technology in healthcare, life sciences and beyond. Quantum technologies will contribute to furthering net zero, climate forecasting, drug discovery, autonomous vehicles, molecular integration, and the development of new materials. Find out more and apply here. Further details on available projects are coming soon.
Further funding opportunities:
- King's-China Scholarship Council
King's-China Scholarship Council PhD Scholarship programme (K-CSC) is open to students from China. Details of this programme can be found on our website.
We welcome applications from students who can self-fund their PhD and they will be supported with a Research and Training Support Grant per annum to support training, attending conferences, and research-related costs.
PhD students are encouraged to contribute to the department's teaching, for which payment will be made separately. Training and mentoring in teaching and learning in higher education is provided by the faculty.
King's-China Scholarship Council PhD Scholarship programme (K-CSC) is open to students from China. Details of this programme can be found on our website.
For further information on postgraduate research funding opportunities and scholarships please visit the King’s Funding Database.
We offer PhD projects under a range of different research themes in pure and applied mathematics. Applicants can explore the funded studentships listed here and apply to ones that suit their interests.
In addition, applicants can also identify more topics and supervisors by looking at the individual research pages of potential supervisors who can be contacted directly. Please see our Funding tab for further information.
Please note the application deadlines on each funded project advert, as these may vary.
Other projects with potential funding
We welcome applications from students who have secured or are applying for other funding (within other studentships internal to the university or external schemes) and from self-funded students. Please see our funding tab (above) for information on PhD funding opportunities. When applying for these projects please specify the name of the supervisor and any relevant funding codes, found on the funding tab.'
Supervisor: Dionysios Anninos
Title: Group theory and the de Sitter universe
Abstract: The project aims to develop the interplay between group theoretic aspects of the de Sitter isometries and quantum fields on a fixed de Sitter background. A particular emphasis will be placed on gauge fields, both of integer and half-integer spin. The structure of entanglement of these fields will be considered.
Supervisor: Chris Herzog
Title: Charting the Landscape of Defect and Boundary Quantum Field Theory
Abstract: Most of the major progress in theoretical physics over the last quarter century is associated with gravity and quantum field theory (QFT) in mixed dimensional systems -- whether that means black hole horizons, topological insulators, D-branes in string theory, twist defects in computations of entanglement entropy, or the interplay between the boundary and bulk in AdS/CFT correspondence. This progress suggests major fundamental gaps in our formulation of gravity and QFT in mixed dimensional systems that cries out for reconsideration and development. The aim of this PhD project will be to chart the renormalization group landscape of quantum field theories in the presence of boundaries and defects. A variety of approaches will be used, from more conventional epsilon expansion and large N to newer AdS/CFT and numerical bootstrap techniques. Results in this project may have direct experimental relevance for graphene and carbon nanotubes and also for flux tubes and Wilson lines in gauge theories.
Supervisor: Petr Kravchuk
Title: Numerical and analytical conformal field theory
Abstract: The goal of this research project is to explore the non-perturbative properties of general conformal field theories (mostly in 3 dimensions and higher) using both numerical and analytical approaches to self-consistency conditions (conformal bootstrap) or effective descriptions, with a view towards applications in critical phenomena, quantum field theory and AdS/CFT correspondence.
Supervisor: NeilLambert
Title: Non-Lorentzian Field theories and Gauge/Gravity duality
Abstract: The mainstream examples of gauge/gravity duality involve Anti-de Sitter spacetimes and field theories with a conformal SO(2,D) symmetry. However in recent years examples have arisen where the field theory is not Lorentzian and the corresponding conformal group is not simply SO(2,d) for some d. This project will explore the construction of these theories and their symmetries at both the level of gauge field theory as well as their gravitational dual geometries.
Supervisor: Sameer Murthy
Title: Black holes and the quantum structure of spacetime
Abstract: Black holes are known to have thermodynamic properties like temperature and entropy. This is an important clue towards a quantum theory of gravity, and explaining these thermodynamic features from a more fundamental quantum-statistical point of view is an active topic of research. The project aims to explore questions about quantum aspects of black holes, within the framework of string theory and AdS/CFT, of the following sort:
(1) What is the nature of the microscopic states underlying a black hole?
(2) How does one describe the collective behavior (phases) of these microstates?
(3) How does one describe the microscopic structure of spacetime from a gravitational path integral?
A good knowledge of quantum field theory (including path integrals) and GR are prerequisites. Some knowledge of string theory is useful, this will be developed as one goes along.
Supervisor: George Papadopoulos
Title: Geometry with applications to physics
Abstract: The projects I have on offer include an exploration of the geometry of the moduli space of connections with a view to apply the results in AdS/CFT. I am also interested in the application of the Perelman's ideas, used in the proof of the Poincare conjecture, to physics.
Supervisor: Gerard Watts
Title: Defects and related structures in two dimensional field theory
Abstract: Defects are ubiquitous in current studies of quantum field theory, providing both new results and fresh insights into old. This project could go in any number of directions in which I am currently working - the mathematical proof of the consistency of the topological defects in fermionic theories; the study of defects related to generalised Gibbs ensembles; the relation to non-invertible symmetries; numerical work on defect perturbations. It would start with the basis of two dimensional conformal and integrable field theory, and the subsequent direction would be decided by mutual agreement.
For full details on how to apply to our research degrees, please see the course pages: