Our main areas of research

• Graph Theory & Combinatorics

• Graph spectra
• Singular graphs; polynomial reconstruction; line graphs of trees
• Possible equations in stoichiometry; applications to the structure of fullerenes
• Graph partitions; main eigenvalues, walks of graphs, self complementary graphs
• Reconstruction, pseudosimilarity and related problems on graph symmetries
• Applications of graph theory to error-correcting codes
• Combinatorics of finite sets
• Independence and domination in graphs

• Mathematical Analysis and Applications

• Subspace structures of inner product spaces as quantum logics
• Non-commutative measure theory
• Measure-theoretic characterisations of topological properties
• Order topologies
• Cardinal Functions
• Selection theory

• Mathematical Physics and Applications

• Random Schrödinger operators with the presence of a random potential in a magnetic field; the theory of self-adjoint operators and probability theory as applied to operators; application to the quantum Hall effect
• The general theory of relativity and relativistic astrophysics
• Plasma physics in magnetically confined fusion plasmas
• Numerical solution of partial differential equations using the finite element and similar methods

• Inverse Problems and Mathematical Modelling

• Development of new technologies for public health and diagnostics;
• Medical imaging techniques including Electrical Impedance Tomography, Microwave imaging, Thermography
• Analytical and numerical methods to solve forward and inverse problems for non-linear partial differential equations
• Integral equation methods
• Regularization methods for ill-posed inverse problems
• Non-destructive testing
• Systems biology and mathematical modelling for biological applications
• Data analysis and visualisation, programming and algorithm development with MATLAB