Projects
The Kneser-Tits problem for linear algebraic groups of type E_8 of relative rank 2 Ghent University
A fundamental problem in the theory of linear algebraic groups is the Kneser-Tits problem. For most groups of relative rank 2, the solution to the Kneser-Tits problem is known. The remaining groups of relative rank 2 for which the problem is unsolved, are two groups of type E_8. Both problems can be reduced to purely algebraic questions. The research in the direction of the study of these problems offers a lot of opportunities.
Von Neumann algebras, group actions and discrete quantum groups. KU Leuven
VNALG: Von Neumann algebras, group actions and discrete quantum groups. KU Leuven
Simple linear algebraic groups: representation theory and subgroup structure KU Leuven
This research project concerns the representation theory and the subgroup structure of simple linear algebraic groups. These two topics are very closely related, as for example the study of subgroups of classical groups is essentially the study of representations of groups. Two major open problems for researchers in this field are understanding the irreducible representations of simple linear algebraic groups and classifying their reductive ...
The study of crystallographic actions and the corresponding orbit manifolds by creating and exploiting connections between the geometrical, topological, group theoretical and Lie algebraic aspects involved. KU Leuven
Braided quantum groups, actions and von Neumann algebras Vrije Universiteit Brussel
Quantum groups, Hopf algebras and tensor categories. Hasselt University
Non-associative algebras for exceptional groups Ghent University
Linear algebraic groups are matrix groups defined by polynomials. In the past century, a lot of research has been done to develop a classification of these algebraic groups. Among the objects of most interest in this theory are the exceptional groups. Though their classification is complete, a lot of questions remain about these mysterious objects.
Recently, a class of algebras that have these exceptional groups as symmetries have ...
Non-associative algebras for exceptional groups Ghent University
Linear algebraic groups are matrix groups defined by polynomials. In the past century, a lot of research has been done to develop a classification of these algebraic groups. Among the objects of most interest in this theory are the exceptional groups. Though their classification is complete, a lot of questions remain about these mysterious objects. Recently, a class of algebras that have these exceptional groups as symmetries have been ...