The Department's main areas of research are:

**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

M.Sc. students have recently worked on topics such as adversary and ally reconstruction numbers, self-complementary graphs, measures of non-planarity, the polynomial reconstruction for disconnected graphs, graphs with end-vertices, crossing number of graphs, and error correcting codes.

**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 Application****s**

- 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

M.Sc. students have also worked on other topics such as the Schwarzschild metric in general relativity, minimal surfaces, stable embeddability of graphs on surfaces, free vibrations in rectangular plates, finite element solution of non-linear problems in elasticity, and self-similar teletraffic models.

**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

25 January 2020

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