The research group Algebra studies group theory, non-associative algebraic structures, and combinatorial and applied algebraic geometry. This includes:
- structurable algebras, linear algebraic groups and related structures in geometry and group theory;
- finite groups, axial algebras and decomposition algebras;
- totally disconnected locally compact groups;
- combinatorial algebraic geometry;
- applied algebraic geometry and algebraic statistics.
The research group Incidence Geometry studies incidence structures, Galois geometry and coding theory, with current research topics:
- polar spaces,
- generalised polygons,
- near polygons,
- partial geometries and their generalisations,
- projective embeddings and non-abelian representations of geometries,
- special subsets in Galois spaces with their translations in terms of codes and links to cryptography.