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:
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.
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
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
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
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