- The research group Incidence Geometry
studies incidence structures, Galois geometry and coding theory,
with current research topics: polar spaces, generalised polygons,
buildings, 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.
- The research group Logic and Analysis
studies mathematical analysis, logic, analytic number theory, computer science and their interrelations.
Current research includes generalised function theory, nonstandard analysis, logical limit laws,
phase transitions for Gödel incompleteness, computer assisted proving and dynamical systems.
- The research group Algebra studies number theory, algebraic
geometry, permutation groups and linear algebraic groups.
Current research in number theory and algebraic geometry is focused on quadratic forms and division algebras
over local function fields, and decision problems concerning the existential theory of function fields;
the geometrical aspect encompasses special divisors on smooth curves,
Weierstrass points, linear systems on blowing-ups and Grassmann defectivity.
Research in group theory is focused on the study of Moufang sets and its connection with Jordan algebras
and other algebraic structures related to linear algebraic groups.
- The research group Differential Geometry and Mechanics deals with the
differential geometric approach to classical mechanics and classical
field theory, and to the study of dynamical systems in general.