Mathematics
School of Mathematics & Physical Sciences
Magnetic quadrupole


At Hull, we have researchers working on a wide range of topics in mathematics, including:

Pure mathematics: Applied mathematics: Probability and statistics:

Asymptotic Geometric Analysis and Probability Theory

Joscha Prochno

Asymptotic Geometric Analysis can be situated at the crossroads of essentially three branches of mathematics: functional analysis, convex and discrete geometry, and probability theory. It studies the geometric properties of finite dimensional objects, normed spaces, and convex bodies and the asymptotics of their various quantitative parameters as the dimension tends to infinity. The theory demonstrates new and unexpected phenomena characteristic of high dimensions. Since high-dimensional systems are very frequent in mathematics and applied sciences, understanding of high-dimensional phenomena is becoming increasingly important. The last decade has seen a tremendous growth of the theory, with the development of new powerful techniques, mainly of probabilistic flavour.

At Hull, our main interests are the local structure of classical Banach spaces (e.g., subspaces of Lp with a symmetric structure, tensor products of Banach spaces), the geometry of (random) convex sets in high-dimensions (e.g., statistics of geometric functionals), the non-asymptotic theory of random matrices (e.g., singular values for several ensembles), large deviation principles and applications to information-based complexity (high-dimensional numerical integration).

Potential Ph.D. projects

  • Singular values of  random matrices
  • Large deviations in Asymptotic Geometric Analysis 

Low-Dimensional Topology 

Jessica Banks

 Knot on a genus-2 handlebody

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? 


Environmental and Industrial Modelling

Tim Scott 

oil extraction

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 fluid jet

John W Elliott 

 

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.

 

 

 

 

 


Superstring Theory 

Ron Reid-Edwards
Daniel Riccombeni

3D projection of a Calabi Yau manifold

The question of how to reconcile Einstein’s theory of gravity with quantum theory is one of the great issues of modern physics. It goes to the heart of what space-time truly is at the smallest quantum scales.

String theory is a theoretical framework that answers some, and perhaps one day all, of these questions. It has also lead to surprising new results in many areas of pure mathematics. Despite many advances in the field, the theory is still very poorly understood.

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.


Foundations of Statistics

Marco Cattaneo

rolling dice

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 PhD research projects include:

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

Statistics in Astrophysics

Siri Chongchitnan

Galaxy Cluster Abel 520

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 for graduate studies include:

-     Superclusters and supervoids.

-     Extreme-value in the inflationary landscape.

-     Understanding extreme solar flares (in collaboration with Sergei Zharkov)

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