Research undertaken in the Department of Mathematical Sciences spans a wide range of key themes within science and technology. Our cutting-edge research uncovers both impactful and exciting outcomes that apply to many aspects of the modern world.

The mathematical sciences often form an 'unseen' part of our everyday lives, yet they underpin many aspects of the modern world. Mathematics is a key driver in advancing many areas within science and technology, making continued research in mathematics both impactful and exciting.

The researchers in our department collaborate with mathematicians, scientists and industry partners from around the globe to deliver top quality research. Our strengths were reflected in the latest Research Excellence Framework (REF) results (2021), where 100% of Mathematical Sciences research impact was rated 'world-leading' or 'internationally excellent'.

The research interests of the group include analysis of partial differential equations (PDEs), including hyperbolic equations and systems with multiplicities, microlocal, spectral and harmonic analysis, eigenvalue estimates for Dirac and Schrödinger type operators, inverse spectral transform method for integrable PDEs, applications to approximation theory, as well as other topics.

This group studies a wide range of aspects of dynamical systems theory, such as Hamiltonian and dissipative dynamics, dynamical chaos in classical and quantum systems, dynamics of multi-scale systems, ergodic theory, random matrix theory, and bifurcation theory.

The research of the group covers a broad range of topics in geometry and related areas of mathematical physics, including the theory of both classical and quantum integrable systems. Another research focus is algebraic geometry, in particular, birational geometry and mirror symmetry.

The group’s interests are in wave motion in a variety of physical situations including geophysical fluid dynamics, water waves, solid mechanics, Bose-Einstein condensates, electromagnetism and acoustics. The group develop and apply exact, numerical, asymptotic and perturbation techniques to pursue research on linear and nonlinear waves with a focus on solitary waves and soliton theory, stochastic wave systems, wave generation, and diffraction and scattering by obstacles.

Members of the group apply a variety of techniques from applied mathematics to diverse problems in medicine, biology, fluid dynamics, materials and soft matter science. The biological systems studied range from intracellular processes to those at the scale of organisms and populations. The fluid flows studied range from environmental buoyancy-driven flows to technologically important micro- and nano-fluidic flows.

The modelling of materials involves the use of mathematical and computational techniques to solve a wide and varied class of problems. This includes nanoscale devices where the fate of individual atoms is important. It spans length scales and time scales that vary over many orders of magnitude and involves the solution of equations that range from continuum to quantum mechanical descriptions.

You can find further details on Mathematical Modelling.

The Statistics group is involved in methodological research in contemporary issues in mathematical and computational statistics, as well as in making diverse applications to the natural, biological and social sciences, including engineering, medical imaging, astrophysics, materials science, ecology, testing theory, etc.