The Applied Mathematics Group at Leicester is a well-established community of researchers and academics working in the areas of Data Analytics and Artificial Intelligence, Numerical Analysis, Mathematical Modelling and their applications. Our mathematical research in these areas is supported and complemented by active and long-lasting industrial and academic collaborations including in Health Technologies and Healthcare, Security, and Space and Earth Observation sectors. We are engaged in joint research with Leicester Institute for Space and Earth Observation, Leicester Space Park, Leicester Precision Medicine Institute as well as with departments and schools across the College and the University.
The group hosts and directs the Visual Intelligence Laboratory and the University-wide Data Analytics, Artificial Intelligence, and Modelling Centre.
Data Analytics and Artificial Intelligence
The group conducts fundamental and applied research in Machine Learning, Artificial Intelligence (AI) and Data Analysis. Mathematical foundations and algorithms for linear and non-linear dimensionality reduction have been a long-standing focus of work in the group, with principal manifolds and principal graphs being examples of methods developed in the group. Other areas of active research interests include the concentration of measure phenomena in high-dimensional spaces, inverse problems, and optimization.
We are actively working on methods and algorithms underpinning a broad range of applications including computer vision, Computer Tomography (CT) imaging, text mining and text analysis, functional data analysis, and portfolio optimization. More recently, and with the advent of the Big Data challenge and explosive growth of data-driven AI systems, the group is driving theoretical and applied research in AI and Machine Learning aimed at addressing the fundamental problems of handling and quantifying inevitable errors in data-driven AI systems across scales and developing resilient, robust, and trustworthy data-driven AI.
The group conducts multidisciplinary research in mathematical methods underpinning physical, chemical, biological kinetics, mathematical ecology and biology. Its research reaches out to high-impact journals including Science, Nature Communications, Physics of Life Reviews and Physical Review Letters. The group contributes to advancing Hilbert’s Sixth Problem through their research on hydrodynamic manifolds for kinetic equations. The second major focus of the group is on mathematical ecology centering on animal behavioural responses, kinesis of animals and microorganisms and plankton-oxygen dynamics under the global climate change.
Examples of the applications and outcomes of our work include applied geophysical problems, modelling of geysers on Enceladus, regulation of protein translation, the baseline theory of long-term transient ecological dynamics, general mathematical theory of biological invasions, discovery and justification of a novel class of nano-devices, a theory of electrostatic collapse of polyelectrolytes in good and poor solvents, a new theory of vector Smoluchowski equations, new phenomena and regimes in aggregation-fragmentation kinetics in infinitely large systems of Smoluchowki-type equations. The latter results enabled to explain the distribution of size of particles in planetary rings like e.g. in the rings of Saturn.
Numerical Analysis at Leicester is focused on the development of novel robust and efficient numerical methods for the accurate simulation of complex problems and their theoretical analysis. New methods have been developed across a broad spectrum of applications, involving multiple spatial and temporal scales. Recent work on numerical methods accepting general meshes involving arbitrarily shaped polytopic computational elements/cell has been at the forefront of this exciting area of research. The group is also known for the development and analysis of automatic self-adaptive algorithms for variational methods of steady and dynamic highly non-linear problems based on mathematically rigorous a posteriori error estimates. Our expertise extends also to aspects of high dimensional approximation and the study of related mathematical questions.
Methods developed by our group have been applied to industrial scale problems ranging from power plant turbomachinery to geophysical applications.
The Applied group welcomes students to study for PhD degrees in any of its research areas. Find out more about PhD degrees in mathematics.