• 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

Resolvent and the polynomial numerical hull

Polynomial numerical hull equals the polynomial convex hull of the spectrum of an operator and it can in principle be computed if the norms of polynomials of the operator are available.

It was noticed that it is more natural to ask for a concrete representation for the resolvent, outside the polynomial numerical hull, rather than trying to compute the set in which such a representation does not exist. This lead to a surprisingly simple general representation of the resolvent operator as a power series, in which the speed of convergence is associated with a Green's function for the outside of the polynomial numerical hull. The representation opens a lot of new questions. The aim is to study in particular the behaviour of the resolvent under analytic perturbations of the operator.

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