Probability and statistics:
At Hull, we have researchers working on a wide range of topics
in mathematics, including:
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
- Large deviations in Asymptotic
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
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
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.
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
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
Potential PhD research projects include:
- Regression with interval data
- Learning from data with graphical models
- An axiomatic approach to likelihood decision making
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
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
in the inflationary landscape.
extreme solar flares (in collaboration with Sergei Zharkov)