Members of the team are engaged in interdisciplinary research in applied mathematics with applications in a number of interlinking industries.
Research is an important activity, ensuring the vitality and health of our academic subjects, and underpins the teaching of our courses.
Members of the mathematics team are engaged in interdisciplinary research in applied mathematics with applications to biomedical, health and life sciences, engineering, computing and industry, specifically in the following areas of mathematics:
- biomathematics, bioinformatics and computational biology
- complex systems and computational neuroscience
- deep learning and biomedical image analysis
- graph theory and combinatorics
- industrial mathematics
- mathematical modelling and numerical analysis
- quantum information science
- statistical learning theory and applications
Bioinformatics and Complex Systems Group
The research of the Bioinformatics and Complex Systems group focuses on the development of novel mathematical and statistical approaches for analysis of data emerging from various disciplines, with especial focus on neuroscience and the biosciences more generally. It aligns with the Allied Health Professions, Dentistry, Nursing and Pharmacy subject area and Health and Wellbeing strategic research theme.
- Emeritus Professor Nadia Chuzhanova's research interests include in silico modelling of mechanisms of mutations underlying inherited disease and cancer, based upon computational statistics and DNA complexity measures. She is particularly interested in the role of repetitive sequences, epigenetic factors and 3D architecture of the human genome in mutagenesis.
- Dr Jonathan Crofts' research is in computational and applied mathematics with strong interests in computational neuroscience. In particular, his current research focuses on developing new mathematical approaches that combine techniques from network science, machine learning and dynamical systems in order to understand complex self-organising systems such as the brain.
- Dr Martin Nelson's research is primarily in the area of Mathematical Biology, with particular focus on biomechanical models and models of complex many-cell systems. Applications to date include morphogenesis of soft tissues, tissue engineering, and sexually-transmitted infections. Current projects include modelling spatial aspects of the anti-inflammatory response via both partial differential equations and cellular automata models, and using techniques from network science and dynamical systems theory to elucidate the mechanisms underlying certain neurological conditions.
- Dr Jason Smith's research interests are in topology and combinatorics, and their applications to neuroscience. In particular, using tools and techniques from topological data analysis and graph theory to understand brain structure and function. He is also interested in other combinatorial problems including permutation patterns, poset theory, and the Abelian sandpile model.
- Dr Keith Smith’s research interests include i) measurement of the complexity of multivariate biological systems with applications to human health and disease, ii) applications of machine learning to large population level neuroimaging data (e.g. UK Biobank, & the Lothian Birth Cohort), and iii) theoretical modelling of networks, and the network mechanisms underlying population characteristic distributions.
Contact for the Bioinformatics and Complex Systems group: Dr Jonathan Crofts.
Computational and Industrial Mathematics
The Computational and Industrial Mathematics research group develop bespoke mathematical and numerical models for problems arising in both engineering and the natural sciences, often motivated by demand from industry end-users. The group has expertise in boundary element methods, computational intelligence algorithms, data-driven methods, equivalent source methods, finite difference methods, finite element methods, pseudo-spectral methods and ray/particle methods including Dynamical Energy Analysis (DEA). Their work contributes throughout the research activities of the Imaging, Materials and Engineering Centre, most prominently within the SOFT and Digital Innovation groups.
- Dr David Chappell's research interests surround mathematical modelling and numerical analysis with industrial applications. Areas of current interest include time-dependent wave propagation problems, boundary integral and boundary element methods, convolution quadrature methods, inverse problems, fluid-structure interaction problems, high frequency wave modelling in complex industrial and engineering structures, numerical methods for phase space flow equations, uncertainty modelling and multi-scale methods. Dr Chappell is a previous recipient of the Vice Chancellor’s Outstanding Researcher Award (early career).
- Dr Archontis Giannakidis’ research lies in the intelligent processing of biomedical and other types of data. He focuses on the development of novel efficient deep learning techniques towards: (i) automating intellectual tasks normally performed by humans, (ii) learning dense data representations, (iii) revealing hidden patterns in the data, (iv) optimising decision-making. He has a particularly strong interest in applying machine intelligence technologies to improve the management of patients with cardiovascular diseases. Another main research area of his is in diffusion tensor MRI.
- Dr Matt Tranter’s research interests are in the area of nonlinear waves, with a focus on the scattering of localised waves in a medium with inhomogeneities such as delaminations in layered waveguides. This research combines numerical solutions of the model (a Boussinesq-type system) and semi-analytical results to simplify the computations. Other areas of interest include the study of initial value problems for nonlinear equations, recently focusing on the issue of zero-mass contradictions, fluid-structure interaction, diffuse-interface models for droplet motion using the Cahn-Hilliard Navier-Stokes equations, propagation of nonlinear periodic waves in layered structures and multi-scale methods.
- Dr Mark Wilkinson is an applied analyst. His research interests lie in atmospheric fluid dynamics, the kinetic theory of particle systems, and the theory of liquid crystals. In particular, his current interests are focused on (i) the analysis of the semi-geostrophic equations (which are PDE used by the Met Office to help predict the weather), and (ii) the analysis of the Boltzmann equation for systems of non-spherical particles.
Contact for the Computational and Industrial Mathematics group: Associate Prof David Chappell.
Mathematical Aspects of Computer Science
The research of the Mathematical Aspects of Computer Science group focuses on the developing mathematical and statistical foundation for a range of computational techniques and approaches. It aligns with the Computing and Informatics subject area.
- Quantum computing research, undertaken by Dr Colin Wilmott, is conducted in entanglement, quantum computing, quantum cryptography, and quantum error-correction – all of which drive new work in the area of quantum technologies. Our investigations are based on innovative, award-winning research – an example of which relates to our novel approach to optimal quantum circuit construction for high performance, miniaturisation and scalability, and makes great use of mathematical aspects from combinatorics and number theory.
- The focus of Dr Golnaz Shahtahmassebi's research is on the development and application of methodology of Statistical Learning Theory and Bayesian Inference to modelling non-Gaussian and non-linear data. Application areas include multispectral image analysis with application to art history and conservation and quality control (defect or crack detection); remote sensing studies (land cover information extraction from satellite images); modelling high latitude ionosphere plasma structure in atmosphere.
Contact for the Mathematical Aspects of Computer Science group: Dr Colin Wilmott.
The Nottingham BBSRC Doctoral Training Programme
You can apply for the Nottingham BBSRC Doctoral Training Programme as a training partnership with University of Nottingham, Nottingham Trent University and the National Biofilms Innovation Centre (NBIC). Find out how to apply here.