• 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

Matrix factorization problems and algebra

Originally motivated by diffractive optics, various matrix factorization problems are under study. Further investigation have give rise to a link between matrix analysis and computations with classical topics in algebraic geometry. For instance, we have a natural concept for the spectrum of a matrix subspace given in terms determinantal hypersurfaces in the complex projective space. Aside from fundamental concepts, these ideas are also being planned to be used in preconditioning large linear systems.

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