The Dreams in the Witch House
I am a mathematician interested in theoretical sciences, especially in applying mathematics to problems in computer science and physics to find practical solutions and deepen the understanding of the underlying structures.
My main research area is geometric modelling and computational geometry. Understanding, describing and handling geometric properties and the shape of solid physical objects and computational models of them has a variety of applications related to computer aided design and also involves interesting theoretical questions. I am particular interested in high level properties of geometric models which can help to simplify computing with them and allow to argue about design intent, functionality and other properties related to the shape of the object. I am working on the robust detection of approximate geometric regularities, such as symmetries and congruences, and enforcing and describing such geometric patterns using geometric constraints and transformations. I am also interested in free-form modelling.
Furthermore, I am working in numerical analysis and artificial intelligence on problems related to geometric modelling. In numerical analysis I am interested in optimization methods, solvers for polynomial equation systems and parallel algorithms. Artificial intelligence techniques are useful for many applications where a precise definition of the required result is hard or impossible or where the exact solution is too expensive to compute. I am particularly working on decision systems which are able to make consistent, intelligent decisions in ambiguous situations similar to human decisions and methods which can automatically learn the behaviour of complex systems.
In addition I am interested in numerical problems in quantum control relating to building quantum computers and questions in quantum information about quantum algorithms, computability and complexity.
