Research Programs in the
Mathematical Sciences Institute
The principal research activities of the MSI, which are administered
through the CMA, are divided into seven programs with the following
main interests:
| Computational Mathematics: analysis of algorithms,
approximation, combinatorics, computational complexity, computational number
theory, data mining, environmental modeling, numerical analysis, numerical
solution of PDEs, optimisation, parallel algorithms, symbolic computation,
randomised algorithms and simulation |
Mathematical Physics and Theoretical Astro-Physics:
string theory, exactly solved models in statistical mechanics, related
combinatorics, spin ladders, chiral Potts model, theoretical morphology and
stromatolites, geometric methods, quantum field theory, modelling of accretion disks, modelling
of stars and stellar atmospheres, and fluid mechanical problems |
| Algebra
and Topology:
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
|
Statistical
Science: applied statistics, bioinformatics, statistical genetics,
biometrics, medical statistics, epidemiology, survival analysis,
bootstrap methods, curve estimation, spatial statistics, data mining
and robust statistical inference
|
| Analysis and
Geometry: 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 pde's and Maxwell's equations
|
Stochastic
Analysis: 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
|
| Applied and
Nonlinear Analysis: nonlinear pde's, variational problems, minimal
surfaces and affine maximal hypersurfaces, monotonicity formulae,
interior second derivative and interior curvature bounds, harmonic
maps, heat flow, and the theoretical aspects of numerical analysis
|
|
In addition, the MSI hosts two virtual centres:
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