Mathematics research degrees

How to applyMathematics

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, and you'll also benefit from being part of a genuine community of mathematicians.


Our key research interests can be broadly themed in to 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.

Low-dimensional topology

Topology is sometimes described as 'rubber sheet geometry'. It is the study of properties that remain unchanged when you are allowed to stretch and bend (but not break) any object freely. Low-dimensional topology focuses on the dimensions we are (reasonably) familiar with from everyday life: 0, 1, 2, 3 and 4. Questions of interest include: how can we quickly identify certain types of object, and in what ways can one type of object sit within another?

Staff: Dr Jessica Banks


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.

Staff: Dr Tim Scott

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

Superstring Theory

At Hull, our main interest is understanding what the true character of quantum space-time is. We study the duality symmetries of string theory and M-theory and employ novel techniques such as twistor theory and doubled geometry to learn more about string theory, M-theory and related quantum field theories. Recent research has focussed on lattice models and scattering amplitudes.

Staff: Dr Ronald Reid-Edwards


Probability and Statistics

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: Dr Marco Cattaneo

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: Dr Siri Chongchitnan

Admissions Status

Open for admission in 2017/18

Research options

PhD: 4 years (full-time)


Home/EU: £4,195 (full-time) / £2,098 (part-time)

Overseas: £15,300 (full-time)

These fees are for all Mathematics research degrees research programmes on this page. For courses lasting more than one year, small annual increases may apply. For more information, please visit

The Postgraduate Training Scheme

It is now widely recognised by employers, professional bodies and research funding agencies that specialist expertise alone is not sufficient preparation either for research or a subsequent career. With this in mind, the University of Hull requires all its postgraduate research students to follow a research training programme relating both to their particular field of study and to generic skills; for example, information technology and communication skills.

Next Steps


For information on scholarships, bursaries and how to fund your studies see our Scholarships and Bursaries page.

Entry requirements

You will need at least the equivalent of a second class Honours degree in mathematics or a related subject.

International students (language requirements)

If you require a Tier 4 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.

This course requires IELTS 6.0 overall, with no less than 5.5 in each skill. For other English language proficiency qualifications acceptable by this University, please click here.

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.


Mathematics staff at Hull are a dynamic team of world-class researchers.

Part of the Faculty of Science and Engineering, we're proud to offer a wide range of innovative undergraduate and postgraduate programmes, delivered in state-of-the-art facilities, as part of our commitment to high quality teaching and cutting-edge research.  

Find out more about research in Mathematics