Mathematicians in the Department have interests in inverse problems, integral equation methods and solutions, computational algebra, mathematical biology, theoretical physics, optimization, mathematical modelling.
Researchers in the group also offer consultancy and training to research-active staff at Oxford Brookes via Mathslink.
The department has a long involvement with Inverse Problems, especially the important inverse conductivity problem. This is concerned with the determination of the electrical conductivity distribution inside a body using electrical measurements on its boundary. While theoretically and practically challenging, it has many possible applications in industrial and medical tomography where it is known as Electrical Impedance Tomography (EIT).
Current work is in the following areas:
- Non-iterative methods using integral equation formulations of EIT that determine the conductivity in a semi-analytic form.
- Estimating the information contained in EIT measurements.
- Using methods of Complex Analysis in two-dimensional inverse problems.
- Medical applications of EIT – design, modelling and construction of an electrical probe for applying optimized electrical stimulation to living tissue.
- Reconstruction algorithms for Electrical Impedance Mammography.
- EIT image of lungs.
Integral Equation Methods and Solutions
Our research focuses on developing integral equation methods for solving partial differential equations and analytical methods for approximating solutions of singularly perturbed Volterra integral and integro-differential equations with weakly singular kernels.
Work in this area includes the development of an efficient algorithm for solving pairs of simultaneous quadratic equations in four variables. This method can be used, for example, to determine the rational points on elliptic curves.
Mathematical Biology research in the Department focuses on population and systems biology. We currently work on:
- Developing modelling frameworks where the spatial aspects of population biology phenomena can be integrated, especially those occurring at different scales (e.g. pollination vs. seed-dispersal; aggregation vs. dispersal).
- Predictive modelling and integrative/systems biology.
Support for research active staff
Statslink/Mathslink provides one to one statistical and mathematical advice for research-active staff within all faculties, supporting joint grant applications, research design and analysis. Appropriate statistical advice can promote better postgraduate learning or supervision and lead to higher quality publications in many subject areas.