Significant research is being carried out in the Department in these areas of Mathematics:
- Graph theory and combinatorics
- Mathematical and computational relativity
- Mathematics of evolutionary biology
- Numerical analysis and uncertainty quantification
- Point patterns and processes
- Quantitative Genetics
- Semiclassical and harmonic analysis
- Stochastic integro-differential equations and their applications
Research group: Mathematical and computational relativity
The group focuses mostly on topics within general relativity (GR) but also has some interests outside this area, in particular in transformation optics, Riemann surfaces for integrable systems of PDEs and the geometry of air-water interfaces. The common theme of the group is the study of the global structure of general relativistic space-times using computational methods. The main tool is the numerical implementation of Friedrich’s conformal field equations in various contexts.
Florian Beyer is interested in mathematical questions in GR and cosmology, such as strong cosmic censorship, the BKL and the cosmic no-hair conjectures. He is developing and using the theory of Fuchsian PDE.
Jörg Hennig studies cosmological models and their causality structure using exact solution methods. He is also well known for his work on fully spectral methods for the numerical solution of hyperbolic PDE.
Leon Escobar Diaz is a postdoctoral fellow and is interested in inhomogeneous cosmological space-times. Particularly, his research is focused on the numerical exploration of the BKL, cosmic censorship and cosmic no-hair conjectures.
Robert Thompson works on transformation optics, electro-dynamics on curved manifolds, the covariant formulation of electrodynamics in ponderable media and analogue space-times.
Apart from the work on the global structure of space-times, Jörg Frauendiener is interested in the Riemann surfaces which appear in the context of integrable systems of PDEs. He is also working on issues of quasi-local mass in GR. A recent interest is the computational determination of capillary surfaces and their applications.