PhD in Mathematical Sciences

Mathematics Research Centre

Algebra

Research work centres on group theory, especially linear groups and algebraic groups, topological and combinatorial aspects of group theory, finite p-groups, computational group theory, and representation theory.

Analysis

Research work centres on harmonic and functional analysis, especially harmonic analysis on groups, operator algebras, infinite dimensional manifolds and holomorphy.

Combinatorics

A very active group that works both on topics within combinatorics (especially finite geometry and design theory) and on links with algebra (permutation groups), logic (model theory), information and coding theory, and design of experiments.

Number Theory and Topology

There are several overlapping areas of activity within the Mathematics Research Centre, for example topology and number theory are not only researched independently, but they are also used as research tools in group theory and dynamical systems.

Dynamical Systems

Areas of current research interest are: dynamics on discrete phase space, bifurcation theory, complex maps, ergodic theory, control systems, spatio- temporal chaos, applications of chaotic systems to packet traffic, thermodynamic formalism, algebraic dynamics, number theory and functional equations.

Statistical Mechanics

Research interests of this group include generalised statistical mechanics methods applied to a variety of complex systems (hydrodynamic turbulence, econophysics, traffic flow, biological and medical applications). The group uses tools from large deviation theory, nonequilibrium statistical mechanics and the theory of stochastic processes.

Relativity and Computation

The Relativity group is a collaboration between the Mathematics Research Centre and the Astronomy Unit. Research interests include: exact solutions of Einstein’s equations and applications of algebraic computing, topological questions, alternative theories of gravity, black holes, and gravitational radiation. Within the Astronomy Unit there is research in cosmology, alternative theories of gravity, and experimental tests.

Probability

The group concentrates on probabilistic problems arising on the interface between Probability and Physics and Probability and Combinatorics. The main research topics are random matrix theory, differential and difference equations with random coefficients, in particular, random Schroedinger operators, Lyapunov exponents, Poisson approximations, and random combinatorial objects.

Statistics

The Statistics group works on the design of experiments, on Bayesian statistics, and on sequential analysis. In the design of experiments there is particular emphasis on applications in the pharmaceutical industry, agriculture, the food industry and chemistry, but the underlying algebraic theory and combinatorial structure are also explored.