The School of Mathematics consists of research groups in Pure Mathematics, Applied Mathematics, Optimization and Statistics. There are around 50 academic staff, 10 research fellows, 60 postgraduate students and 600 undergraduate students. This makes our 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.

Optimization and Combinatorics are two research areas in the School which lie at the interface between Mathematics and Computer Science.

The main focus of the Optimization group is on mathematical theory and methods applicable to managerial decision-making, particularly non-linear and discrete. In collaboration with Computer Science, rigorous and heuristic approaches to multidisciplinary optimization are investigated, with applications in many disciplines. Research covers areas of theoretical, computational and applied optimization, including large-scale nonlinear and semidefinite optimization, discrete optimization and max-algebras, semi-infinite and multi-criteria optimization, equilibrium systems.

The Combinatorics group in Birmingham works mostly in graph theory, extremal combinatorics, as well random discrete structures and algorithms. Recent research in extremal combinatorics has focussed on using probabilistic methods to solve several long-standing problems on Hamilton cycles as well as generalized 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.

Other main research activities of the School can be summarized as follows:

Pure Mathematics

There are subgroups working in algebra, analysis, and combinatorics. The main focus of the algebraists in Birmingham is group theory, including profinite groups, groups acting on trees, construction and generation of sporadic simple groups, and representations of groups. The analysis group at Birmingham has particular strength in harmonic analysis and its interactions with geometric analysis, geometric measure theory, combinatorics, and linear and nonlinear partial differential equations. There is significant further activity in real and functional analysis, discrete dynamical systems and general topology.

Applied Mathematics

The main interests of the group are fluid mechanics, mathematical chemistry & reaction-diffusion systems and mathematical biology. In fluid mechanics, we study free surface flows, bubble dynamics, biological fluid mechanics, moving contact lines and hydrodynamic stability. In the related areas of mathematical chemistry and reaction diffusion systems there is research into cement hydration, micelle formation, solid oxide fuel cells, chemical waves and clock reactions.

Statistics

The main interests of the Statisticians in Birmingham are multivariate nonparametric statistics, nonparametric smoothing and wavelet based methods, time series analysis, mutual information, statistical computing, applications in bioinformatics and neuroscience. 

For more details on School of Mathematics please see the School’s homepage.

Computer Science at Birmingham dates back to the late 1950’s with the School of Computer Science becoming one of the first academic departments in the UK to undertake research and teaching in this field. The School has around 40 academic staff, 25 research fellows, 80 PhD students and approximately 400 undergraduate and postgraduate students. Our research programmes are supported by a wide range of bodies, including UK and EU research councils, overseas governments and universities and UK and multi-national companies.

The School has a particularly strong reputation in theoretical research, which covers a number of different areas:

• Foundational theory of computation: programming languages and semantics (including concurrent systems); domain theory and applications of topology to computation (for example, exact real-number computation); topos theory (especially as applied to quantum physics and quantum computation).
• Logic and algebra: algebraic structures (such as loops and quasi-groups); computational algebra and theorem-proving; logic and model-checking (with applications to security); topological aspects of logic.
• Algorithms: optimization and heuristic search (design of algorithms and their run-time analysis); theory of evolutionary computation; data analysis and data mining.

The main research activities of the School can be summarized as follows:

• Nature-Inspired and Intelligent Computation: The main interests of this group are natural computation (the study of computational processes inspired by nature), machine learning and data mining (making sense of large data sets), medical image interpretation, theorem proving.
• Intelligent Robotics: Interests include computer vision, recognition, task planning, reasoning under uncertainty, and cognitive architectures.
• Computing Systems: The research interests of this group include security protocols, access control systems, applied cryptography, software security, distributed simulation, distributed virtual environments, multi-agent systems, dynamic data driven application systems, computer architectures, peer-to-peer systems as well as grid computing and e-Science.
• Theoretical Computer Science: The focus of this group is on mathematical foundations of computer science such as domain theory, exact numerical computation, computational logic and logic of topology and toposes, as well as on the semantics and formal methods for programming languages.
• Software Engineering: The main interests of this group include automated and distributed software engineering, security software engineering, search-based software engineering, modelling, testing, theoretical and formal aspects of software engineering, robotics software engineering.
• Human-Computer Interaction: including mobile computing, interaction technologies, usability and design, research on natural language processing and understanding, document and text analysis.

For more details on School of Computer Science please see the School’s homepage.