Research programs

Computational Mathematics program

Key topics: Computational number theory, large scale computations, numerical solutions of partial differential equations, optimisation, parallel algorithms, regularisation of inverse problems.

Mathematical Physics program

Key topics: string theory, exactly solved models in statistical mechanics and quantum field theory, related combinatorics, low-dimensional quantum systems, geometric methods, theoretical morphology and stromatolites.

Theoretical Astrophysics program

Key topics: Compact stars: White Dwarfs, Neutron Stars (pulsars and magnetars ) and Black Holes. Radiation processes and transfer mechanisms in accretion flows on to highly magnetic compact stars.

Statistical Science program

Key topics: applied statistics, bioinformatics, statistical genetics, biometrics, medical statistics, epidemiology, survival analysis, bootstrap methods, curve estimation, spatial statistics, data mining and robust statistical inference

Stochastic Analysis and Risk Modelling program

Key topics: applied probability with interests in general properties of a range of models as well as in particular models; applications include mathematical finance, telecommunication systems and epidemics

Algebra and Topology program

Key topics: algebraic geometry, algebraic K-theory, number theory and homotopy theory, as well as the more traditional areas of finite and discrete groups, and representations of Lie algebras

Analysis and Geometry program

Key topics: several complex variables, Banach algebras, spectral theory of operators, harmonic analysis on Lie groups, manifolds and Lipschitz surfaces, microlocal analysis on manifolds with corners, non-commutative geometry, and applications to PDEs and Maxwell's equations

Applied and Nonlinear Analysis program

Key topics: nonlinear elliptic and parabolic PDEs, calculus of variations, applications to differential geometry and geometric evolutions, optimal transportation and geometric optics; fractal analysis and geometry, dynamical systems; associated computation.