Our research

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

https://www.um.edu.mt/science/maths/ourresearch