Mathematics

The School of Mathematics consists of research groups in Pure Mathematics, Applied Mathematics, Optimisation and Statistics. There are currently around 50 academic staff, 12 research fellows, 70 postgraduate students and 700 undergraduate students. This makes the School one of the largest Schools of Mathematics in the UK. Our research involves international and multidisciplinary collaboration and is supported through a wide range of funding bodies as well as the Birmingham Mathematical Institute.

In Pure Mathematics there are major research groups working in Algebra, Analysis, and Combinatorics.

• The Algebra Group at Birmingham is internationally renowned for its research in group theory and representation theory. Significant research has been completed in to the representation theory of finite groups, algebraic groups, Lie algebras and related algebras.  There has been major research on the interaction between group theory and geometry, in particular actions of groups on geometric structures.  In addition, there is active research into the structure of finite groups, especially finite simple groups.
• The Analysis Group at Birmingham is well-known for its particular strength in Euclidean harmonic analysis, with emphasis on the interactions of the subject with a variety of closely related areas, including geometric analysis, geometric measure theory, combinatorics and linear/nonlinear partial differential equations. There is significant further activity in real and functional analysis, discrete dynamical systems and general topology.
• The main research interests of the Combinatorics Group lie in graph theory, extremal combinatorics, as well random discrete structures and algorithms. Recent research in extremal combinatorics has focused on using probabilistic methods to solve several long-standing problems on Hamilton cycles as well as generalised matching problems. An additional focus is on random structures. Here the research is on the average case analysis of algorithms, the evolution of random discrete structures as well as on random models for complex networks.

The Applied Mathematics group has expertise in a wide variety of areas and has collaborations with researchers from industry, healthcare, and other areas of science and engineering. The primary research interests of the group include:

• Nonlinear Waves;
• Reaction-Diffusion Theory and Applied Analysis,
• Asymptotic Methods;
• Fluid Mechanics, Aerodynamics, Stability, Free Surface Flows, Bubble Dynamics;
• Mathematical Biology, Systems Biology and Biofluids;
• Mathematical Modelling in Chemical Engineering;
• Inverse Problems;
• Numerical Analysis and Scientific Computing.

Of particular resonance with the current theme is the activity in Mathematical Biology. The School of Mathematics has a small but expanding mathematical biology group which is strongly integrated with experimental research. Research spans multiple scales from biomechanics down to sub-cellular modelling, including multiscale modelling. Areas of current active collaboration include growth, reproduction and development, fertility, plant science, synthetic biology, drug design and delivery, tissue engineering and medical applications including trauma and immunology in conjunction with the new Queen Elizabeth Hospital, one of the largest academic-trust based hospitals in the world.

The main focus of the Optimisation Group is on mathematical theory and methods applicable to managerial decision-making, particularly non-linear, discrete, and multi-criteria optimisation. Research covers areas of theoretical, computational and applied optimisation, including large-scale nonlinear and semidefinite optimisation, discrete optimisation and max-algebras, semi-infinite and multi-criteria optimisation, and equilibrium systems.

The main interests of the Statistics Group lie in multivariate nonparametric statistics, nonparametric smoothing and wavelet based methods, statistical computing, applications in bioinformatics, medical sciences, economics and neuroscience.

The biostatisticians in the College of Medical and Dental Sciences are organised in 5 teams, in total employing over 40 statisticians based either in the School of Cancer Sciences or the School of Health and Population Sciences.   

A major focus of the biostatistics research is on methodology for clinical trials.   The College hosts the prestigious MRC funded Midlands Hub for Trial Methodological Research which has an active research programme in collaboration with the biostatistics teams based in the three College Clinical Trials Units (CTUs). Key areas of research include the design and analysis of trials for stratified medicine evaluations, Bayesian methodology applied to early phase trials, methods for survival analysis incorporating health related quality of life and cluster randomised trials.  The close collaboration with the CTUs ensures integration of methodological and applied work and provides opportunities for evaluating and applying new methodologies in important clinical studies. Further methodological developments in trials linking to health economic methodologies are based in the Health Economics Unit with the School of Health and Population Sciences.

The Public Health Biostatistics team has major focuses on biomarker and test evaluation, including methods for the evaluation of diagnostic, prognostic, monitoring and predictive tests.   A second strong theme in the group is on methods for meta-analysis, including individual patient data and multivariate methods. Linking the two, the unit is the home of the Diagnostic Test Accuracy activity of the Cochrane Collaboration, providing leading guidance on methodologies for systematic reviews and meta-analysis of test evaluation. Research activity in the group is funded by MRC and NIHR project grants and fellowships.

There are active collaborations with statisticians based in the School of Mathematics both in teaching and research activities.

The College of Life and Environmental Sciences has invested heavily in state of the art infrastructure for high-throughput, high content biology, in particular in the “omics” fields of genomics and metabolomics. These technologies are enabling an unprecedented view of the molecular level functioning of living organisms and their interactions with the environment. In particular the University is world leading in the applications of these technologies to study the effects of environmental stressors, including pollution and climate change, on organism health. Central to these activities is the field of Systems Biology, which utilises a range of mathematical and computational approaches to model and ultimately predict how organisms and populations respond to their natural environment. Increasingly researchers in the College are integrating multiple “omics” datasets and linking these data to measurements on the whole organism and to environmental physico-chemical conditions, while working towards the challenging goal of population and ecosystem modelling. This progress is being mirrored by advances in network inference, temporal analyses, evolutionary computing and Agent Based Modelling. A range of organisms are studied, from microbial biofilms to higher animals including Daphnia and fish.

The current work is funded largely through the NERC with strong links to the Environment Agency and Defra, and internationally with the USA, China and several European countries. In addition the University has just invested ca. £2M into Environmental Genomics research, including a new Chair and associated academic posts, post-doctoral fellowships, technicians, doctoral students and further expansion of the impressive genomics and computing facilities. These activities are focused in the Centre for Systems Biology, which provides a physical space to promote interdisciplinary interactions between mathematicians, computer scientists and biologists, as well as in the School of Biosciences and School of Geography, Earth and Environmental Sciences.

Key researchers - School of Biosciences:

• Professor Mark Viant
• Professor John Colbourne
• Dr Jan Kreft

Some key recent references:

• The ecoresponsive genome of Daphnia pulex.
• Functional and evolutionary insights from the genomes of three parasitoid Nasonia species.
• Towards a system level understanding of non-model organisms sampled from the environment: a network biology approach.
• Identifying health impacts of exposure to copper using transcriptomics and metabolomics in a fish model.
• Discovery and validation of metabolic signatures for predicting whole organism toxicology.