The Mathematical Sciences Institute offers the following supervisors for 2009-2010 Summer Research Scholars. A link from that person will provide a list of the topics of interest that person can offer for potential research scholars.

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. Read more...

Jim Borger Number theory and Algebraic Geometry

Bryan Wang Introduction to Lie groups; Introduction to Differential Topology; Introduction to Dirac operators (Clifford algebras and Spin geometry); Differential forms and de Rham cohomology; Gauge theory and low dimensional topology; Topological quantum field theories.

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. Read more...

Professor Alan Carey - Algebras of operators and their invariants: C*-algebras, von Neumann algebras, algebras of pseudodifferential operators.

Dr Andrew Hassell - Can you hear the shape of a drum?; The spectrum of a triangle -- is it simple?; Scattering theory and Levinson's theorem.

Professor Michael Eastwood - The mathematics of wallpaper design; The geometry of straight lines in three-space; Consequences of the triangle inequality; Differential equations governing circles on the sphere; The geometry of webs in the plane.

Dr Adam Rennie - Algebras of operators and their invariants: C*-algebras, von Neumann algebras, algebras of pseudodifferential operators.

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. Read more...

Professor John Urbas - Various topics in partial differential equations and/or differential geometry involving nonlinear partial differential equations. This includes problems such as finding surfaces of least area spanning a given boundary, and optimal transport (mapping one mass distribution to another one so that some cost is minimal). Topics of a more introductory nature in partial differential equations or geometry are also possible.

Dr Ben Andrews - Differential geometry; Differential equations and Calculus of variations

Professor Michael Barnsley - Fractal Geometry

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. Read more on Mathematical Physics or Theoretical Astro-Physics

Professor Murray Batchelor - Topics in Mathematical Physics

Professor Dayal Wickramasinghe - TBA

Dr Lilia Ferrario - Observational and theoretical aspects of accretion discs in Cataclysmic Variable Stars; Radiation processes and transfer mechanisms in accretion flows on to highly magnetic compact stars; Ultramassive White Dwarfs and the origin of Type Ia Supernovae; The Origin of Magnetic Fields in White Dwarfs and Neutron Stars.

Applied statistics, bioinformatics, statistical genetics, biometrics, medical statistics, epidemiology, survival analysis, bootstrap methods, curve estimation, spatial statistics, data mining and robust statistical inference. Read more...

Professor Alan Welsh - Modelling occupancy and detection; Prediction of random effects.

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. Read more...

Dr Markus Hegland - The numerical solution of elliptic and parabolic partial differential equations with finite elements and wavelets