The following specialisations are available within this research area:
- Ordinary and partial differential equations
- Functional analysis
- Analytical and computational spectral theory
- Quantum mechanics
- Number theory and its applications
- Mathematical physics
- Operator algebras
- Algebraic geometry.
Three research networks have been coordinated from Cardiff:
- the EU-TMR Network on Non-Commutative Geometry
- the EPSRC Network on Algebraic Geometry, Boundary Conformal Field Theory and Non- Commutative Geometry
- the EPSRC Network on Spectral Theory (jointly with a group from the School of Computer Science).