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On this page you can find out about PhD opportunities currently available in Mathematics and Statistics. Click on a project title or research area below to find out more.

Some of these projects come with specific funding (eg, from a research council or Centre for Doctoral Training) to cover your tuition fees and living expenses. If you successfully apply for one of these projects, and you meet the eligibility requirements, you will be automatically awarded the funding. These projects are marked 'FUNDED' in the list below.

If a project does not come with specific funding, that does not mean that there is no funding available. You may be awarded a scholarship after you have submitted your application – let us know if you wish to be considered for a scholarship by including this in your application form. We also accept applications from students who are applying for funding separately, or have funding in place already.

You can find out about scholarships on the following webpage:

Do you have your own idea for a project?

Find a potential supervisor by visiting our research webpages. Contact a member of academic staff to find out about PhD opportunities in their area.


Centres for Doctoral Training

Other funded PhD opportunities are available through the Centres for Doctoral Training or Doctoral Training Partnerships that our staff contribute to.

Visit the webpages for these centres to find out more about their projects.

Centres for Doctoral Training at the University of Sheffield

Once you have identified a potential project and supervisor, please complete the University's postgraduate online application form to apply. If you wish to be considered for a scholarship, you should state this in the form. You should also include any information you have about funding that you are applying for separately, or that you have in place already. It is a good idea to contact the supervisor of any PhD opportunity you want to apply for, before you submit your application.

Postgraduate online application form

Current projects:

Mathematical modelling of tissue self-assembly

Supervisor: Dr Alexander Fletcher

Funding and eligibility: There may be funding opportunities for UK and EU students who meet the UK residency requirements. Please email Dr Fletcher to find out more.

How tissues self-assemble, and how different cell types are established and maintained in such tissues, are fundamental questions in developmental biology with profound implications for tissue engineering and regeneration strategies. While the signalling molecules involved are increasingly well characterised, we still lack a mechanistic understanding of the contribution and timing of short- vs long-range signalling, and their effect on cell proliferation and adhesion. Alongside experimental studies, mathematical models help challenge and refine our understanding of these processes.

Building on recent work by myself and others (Fletcher et al, 2017; Osborne et al, 2017), this project will develop new models of tissue growth and patterning, incorporating multiple signalling mechanisms (autocrine, juxtacrine, paracrine). Detailed analysis will identify how different modes of tissue self-assembly emerge from combinations of these mechanisms in time and space. This work will be applied to the hypothalamus, which regulates core body processes that are essential for survival. Informed by recent findings by Prof. Marysia Placzek (based in the Department of Biomedical Science) on hypothalamus self-assembly (Robins et al, 2013; Fu et al, 2017), and in vitro organoid data that recapitulates development in vivo. Models will be developed to understand whether and how local versus longer-range signalling events underlie hypothalamic cellular homeostasis, cellular architecture and self-assembly.

This interdisciplinary project would involve the development and analysis of ordinary and partial differential equation models, and/or cell-based models, of tissue growth and patterning. It would suit a student with undergraduate training in the physical sciences and an appreciation of the importance of mathematical modelling in the life sciences.

Fletcher AG, Cooper F, Baker RE. Mechanocellular models of epithelial morphogenesis. Phil. Trans. R. Soc. B. 2017 May 19;372(1720):20150519.

Osborne JM, Fletcher AG, Pitt-Francis JM, Maini PK, Gavaghan DJ. Comparing individual-based approaches to modelling the self-organization of multicellular tissues. PLoS computational biology. 2017 Feb 13;13(2):e1005387.

Robins SC, Stewart I, McNay DE, Taylor V, Giachino C, Goetz M, Ninkovic J, Briancon N, Maratos-Flier E, Flier JS, Kokoeva MV. α-Tanycytes of the adult hypothalamic third ventricle include distinct populations of FGF-responsive neural progenitors. Nature communications. 2013 Jun 27;4:2049.

Fu T, Towers M, Placzek MA. Fgf10+ progenitors give rise to the chick hypothalamus by rostral and caudal growth and differentiation. Development. 2017 Sep 15;144(18):3278-88. 10.1242/dev.153379

Statistical inference for misspecified mechanistic models

Supervisor: Prof Richard Wilkinson and Prof Jeremy Oakley

Funding: This studentship is supported by Microsoft Research and EPSRC through Microsoft’s PhD Scholarship Programme. It will provide up to 4 years of funding with an enhanced stipend of £18,777 per annum, and comes with a generous training budget for conference travel to UK and international meetings, as well as for time spent visiting Microsoft Research in Cambridge.

This studentship is available to UK and EU students who meet the UK residency requirements. Applicants should have a good first degree in maths, computer science, or physics.

Mechanistic or simulation-based models are used in scientific research to understand complex natural phenomena. A mechanistic model can take the form of ordinary/partial/stochastic differential equations and can be rigid in form but have the benefit to the scientist of having interpretable and testable parameter settings. In part due to the inflexibility of the model forms, misspecification of the model can lead to computationally expensive inference procedures, and more importantly, misleading conclusions, whereby the parameter estimates are confidently incorrect. There is increasing evidence that the inference framework called approximate Bayesian computation (ABC) is more robust to model misspecification than other inferential approaches. We propose to study the mathematical and statistical properties of this robustness, and explore improvements of current approaches for dealing with model misspecification. The research will be pragmatic, embedding the theory with practical examples (where domain knowledge is understood, and hence misspecification can be detected), including using semi-mechanistic models that are used in the public health domain.

This project will be jointly supervised by Professor Richard Wilkinson (University of Sheffield) and Dr Ted Meeds (Microsoft Research (MSR) Cambridge). The student will be expected to spend some time visiting MSR Cambridge.

Other project opportunities:

If you would like to find out about PhD opportunities in an area that is not covered in the listing above, visit our Research webpages. These pages list the research interests and contact details of our academic staff, so that you can get in touch and discuss other potential projects in their field.


Entry requirements

We usually ask for either a first class or upper second class (2:1) MMath or MSc degree or equivalent in mathematics, statistics, physics or a related subject. We offer a number of MSc courses in mathematics and statistics, if you do not already have a masters degree: Masters courses

Our decision on whether to offer you a place will also be based on the research proposal or personal statement you submit, your degree transcripts (and certificates, if available), your masters dissertation/project (if applicable), your CV and academic references (including your masters dissertation/project supervisor, if applicable), and any interviews and additional tasks we ask you to complete. All documents need to be provided in English, including transcripts and references. Students will also need to meet our English language requirements, and international students will need to get clearance through the Academic Technology Approval Scheme (ATAS). Find out more about English language requirements and ATAS on our webpage for international students:

International students