• Algebra and combinatorics
• Computer aided teaching
• Decision analysis
• Differential geometry
• Dynamic game theory
• Evolution equations
• Finite elements
• Inverse problems
• Nonlinear PDEs
• Numerics
• Stochastics
• System theory
• Systems and operations reserach
• Systems intelligence
• Time-frequency analysis

Computation of hyperbolic structures

In the long time behaviour of dynamical systems the so called SRB measure has a deep meaning. Computation of this eigenmeasure of the Ruelle operator is a highly nontrivial, but important, task. In collaboration with Sergey Pilyugin (St.Petersburg), we are starting a study of connections between this measure and hyperbolic structures of invariant sets. This may lead to numerically efficient approaches for these computations.

The numerics group

Current research topics

• Resolvent and the polynomial numerical hull.

• Local spectral theory

• Complexity issues in computing the spectrum

• The Arnoldi method and polynomial numerical hull

• Boundary conditions and low rank perturbations

• Real linear operator theory

• Density function computations

• Computation of hyperbolic structures

• Level set methods

• Large scale numerical linear algebra

• Matrix factorization problems and algebra

• Algorithmic diffractive optics

• Geometric integration

• Multibody mechanisms