The Department of Mathematics contains three research groups undertaking fundamental research in pure and applied mathematics:
The representation theory group focuses on modern aspects of the representation theory of finite groups, algebraic groups and related algebras, drawing motivation from geometry, statistical mechanics string theory.
The mathematical physics group focuses on quantum mechanics, quantum field theory, string theory and fluid dynamics. One of the distinguishing features of the mathematical physics group is its strong expertise on integrable systems.
The Mathematical Biology group applies mathematical methods to increase our understanding of the biological world, and the central focus is on the mathematical modelling of evolution. There are three main areas of research: evolutionary game theory, cultural evolution, and the modelling of evolution on networks.