In many areas of scientific and industrial research, the mathematical modelling of physical and biological processes leads to complicated sets of differential equations and large networks of interrelated components.
Understanding how to analyse these networks and sets of equations is key to gaining insight into the real-life systems they are modelling.
Rigorous mathematical analysis of these systems can provide crucial understanding of the behaviour of the system and the validity of the model. For instance, it is often possible to determine whether there is more than one solution to a mathematical model or even if a solution exists.
The Applied Analysis Research Group is involved in this development of rigorous analytic and constructive methods for solving differential and integral equations arising from the applied sciences.
Our group has many collaborations with other groups in our department and with researchers from a wide range of other disciplines, from physicists, chemists and engineers to social scientists.
The group has a particular focus on nonlinear evolutionary processes, operator theory for the study of differential and integral equations, and the analysis of networks.
If you're interested in collaborating with us or wish to enquire about postgraduate or postdoctoral research positions then please contact one of the group members listed below.
Specific areas of interest
- application of semigroup theory to coagulation-fragmentation equations and diffusion equations on networks
- qualitative theory of non-linear dynamical systems in material science and mathematical biology
- fractional integral transformations, including the fractional Fourier transform
- differential equations with singular coefficients
- spectral problems that depend nonlinearly on eigenvalue parameters
- spectral graph theory
- mathematical chemistry
- operator theory on graphs and networks
- algebraic topology of networks
- geometric embedding of graphs and networks
- matrix functions for graphs and networks
- diffusion--normal and anomalous--on networks
- inverse problems