Faculty of Science and Engineering

Mathematics research degrees

Postgraduate - Research


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About our programmes

Mathematics at Hull offers opportunities to study towards a Doctor of Philosophy (PhD) in a thriving research environment. We welcome research proposals in any of our specialisms. Our staff have a wide range of expertise in many different areas, from pure maths theories around low-dimensional topology and asymptotic geometric analysis, to fluid dynamics, superstring theory and astrophysics across other disciplines.

While studying towards a PhD at Hull, you’ll be fully supported by two supervisors who are able to offer expert supervision in your area. You'll also benefit from being part of a genuine community of mathematicians.

Apply for a research programme in Mathematics


Open for admission in 2024/25

Qualification Full time Part time
PhD 3 years* 5 years*

* The length of programme registration will be longer as it includes the maximum writing-up phase.

Start in January, May or September


Our key research interests can be broadly themed into the following:

Pure Mathematics

Asymptotic geometric analysis

Asymptotic Geometric Analysis studies the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies and the asymptotics of their various quantitative parameters as the dimension tends to infinity.

At Hull, our main interests are the local structure of the classical Lp spaces, in particular the finite-dimensional normed subspaces with a symmetric basis, the geometry of random polytopes in isotropic convex bodies, and the singular values of random matrices, especially when the random entries are not identically distributed.


Applied Mathematics

Environmental and Industrial Modelling

Environmental mathematical models have been developed to analyse river flows in estuaries and the impact on the growth of vegetation due to pollutants released further upstream. Work has also been done into the feasibility of underground repositories for storing materials with low and medium levels of radioactivity.

Additional interests are in numerical methods for solving large systems of linear algebraic equations underlying environmental models and investigating genetic algorithms for optimisation purposes.


Fluid Dynamics

Within the area of fluid mechanics, the main focus is on a combination of asymptotic analysis and numerical methods for the study of high Reynolds number viscous flows.

Staff: Dr John W Elliott 


Probability and Statistics

Processes on complex networks

Large complex networks can be found everywhere, for example as social, information, technological and biological networks. Many of these networks share the property that they are scale free, i.e., the number of links of nodes have a power law distribution. Hubs with a very high number of links play an important role in the behaviour of the network.

Processes on these networks one can think of are opinion formation in social networks, the spread of information via telecommunication and computer networks, and epidemics in society. In Hull, we use probability theory to investigate what the effect is of the scale-free nature of complex networks on processes on these networks, both in and out of equilibrium.

Potential projects include investigating:

  • Properties of complex networks and random graphs
  • Interacting particle systems on random graphs
  • Metastability in interacting particle systems

Foundations of Statistics

We study the mathematical modelling and management of uncertainty, in which a central role is played by probability distributions. Questions of interest include: what and how can we learn from statistical data? How can we combine different sources of uncertain information? And how can we use such information in order to make optimal decisions in situations involving uncertainty?

 Potential projects include:

  • Regression with interval data
  • Learning from data with graphical models
  • An axiomatic approach to likelihood decision making

 Staff: tbc

Statistics in Astrophysics

What is the mass of the most massive object in the Universe? What is the size of the biggest cosmic void we are most likely to observe? What is the magnitude of the most energetic solar flare that could occur?

We address these questions by studying the likelihood of rare, extreme events with extreme-value statistics, which has long been used in meteorology and engineering, and has recently found many applications in astrophysics.

 Potential projects include:

  • Superclusters and supervoids
  • Extreme-value in the inflationary landscape
  • Understanding extreme solar flares

 Staff: tbc

Fees and funding


Full time:
£4,712 per year

Part time: £2,356 per year

  • EU/International: £16,500 (full-time)

These fees are for all research degree programmes on this page. For courses lasting more than one year, annual increases apply. For more information, please visit the fees and funding page. 

Postgraduate research programme structures


  • Full-time: 3 years of research, with up to 12 months writing up if required
  • Part-time: 5 years of research, with up to 20 months of writing up if required


  • Full-time: one year of research, with up to 12 months writing up if required
  • Part-time: 2 years of research, with up to 24 months of writing up if required

Writing-up and thesis submission

A standard full-time PhD programme comprised three years of research plus up to 12 months of writing-up. Part-time is five years plus up to 20 months writing-up if needed. Full-time standard Masters programmes are comprised one year of research plus up to 12 months of writing-up if needed; and part time Masters programmes have two years of research with up to two years of writing-up.

For full-time students, the writing-up phase typically takes about three months but may be extended to one year without further paperwork. For part-time students, writing-up typically takes one year, but may be extended to two years without further paperwork. The maximum writing-up period is included in your overall programme length, which means that international PGRs will not need to apply for an additional visa to cover the writing-up phase.

If you need to move into the writing-up period of your research degree, you must enrol for this phase and you will be liable to pay a continuation fee.

The fees for the writing-up period for 2023/24 are:

Full time

  • Writing-up fee £345
  • Rebate for submission within first 3 months of the research period end date 100%
  • Rebate for submission between 4- 6 months of the research period end date 50%
  • Rebate for submission between 7-9 months of the research period end date 25%

Part time

  • Continuation Fee £170
  • Rebate for submission within first 3 months of the research period end date 100%
  • Rebate for submission between 4- 6 months of the research period end date 50%
  • Rebate for submission between 7-9 months of the research period end date 25%

Thesis submission timelines

It is expected that you will submit your thesis within the timeframes outlined below:

Masters degrees

  • Submission by one year and 3 months full-time.
  • Submission by 2 years and 6 months part-time.

Doctoral degrees

  • Submission by 3 years and 3 months full-time.
  • Submission by 5 years and 6 months for part-time.

Doctoral Loan

UK students who haven’t secured a scholarship can take out a Doctoral Loan to help with tuition fees and living costs. They provide up to £29,390 for full-time and part-time PhDs in all subject areas.

EU students starting a course on or after 1 August 2021 must have settled or pre-settled status under the EU Settlement Scheme to get student finance. Irish citizens do not need to apply for a visa or to the EU Settlement Scheme.

Additional costs

There are some extra costs that you may have to pay, or choose to pay, depending on your programme of study and the decisions you make. The list below has some examples, and any extra costs will vary:

  • Student visas (international students).
  • Books (you’ll have access to many books through the University library, but you may want to buy your own copies).
  • Optional conference/field/archive/library trips (Faculties support some travel and conference attendance financially. Details vary. Please check with the Department/School to which you are applying).
  • Laptop (you’ll have access to laptops and PCs on campus, but you may want to buy your own).
  • Printing and photocopying (There is a printing allowance in place for all students, currently £20 a year. Some Faculties grant PGR students access to printing and photocopying as staff. Please check with the Department/School to which you are applying).
  • Professional-body membership.
  • Graduation (gown hire and photography).

Remember, you’ll still need to take into account your living costs. This could include accommodation, travel and food – to name just a few.

Some postgraduate research students may be asked to pay a bench fee in addition to the tuition fee to cover additional costs of their research project. If such a fee is levied for additional project-specific costs, not included in the tuition fee, you will receive further information during the application process.

For information about bursaries and how to fund your studies see our money page, or take a look at our PhD scholarships page for specific funded PhD opportunities.

Watch: find out more about postgraduate study at the University of Hull.

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The University’s Postgraduate Training Scheme (PGTS) provides a range of generic and discipline-specific modules to support research students through their programme.

Find out more

The library has an exclusive lounge for postgraduate research students and a dedicated Skills Team to provide a wide range of study and research skills help.

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The Doctoral College provides support to postgraduate research students. Offering skills development opportunities and dedicated facilities, the school is here to help you achieve your potential.

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Research at Hull tackles big challenges and makes an impact on lives globally, every day. Our current research portfolio spans everything from health to habitats, food to flooding and supply chain to slavery.

Find out more

Entry requirements

You should normally have, or expect to obtain, at least 2:1 Honours degree (or international equivalent) in mathematics or a related discipline appropriate to your intended research.

Please contact your prospective supervisor in the first instance. Once a member of staff has agreed to supervise your research project in principle, please make a formal application.

International students

If you require a student visa to study or if your first language is not English you will be required to provide acceptable evidence of your English language proficiency level.

  • For 2024 entry, this course requires IELTS 6.0 overall, with no less than 5.5 in each competency.
  • For 2025 entry, this course requires IELTS 6.5 overall with no less than 6.0 in each competency.

See other English language proficiency qualifications accepted by this University.

If your English currently does not reach the University's required standard for this programme, you may be interested in one of our English language courses.

Visit your country page to find out more about our entry requirements.