# Research Groups

*Incidence Geometry*
studies incidence structures, Galois geometry and coding theory,
with current research topics: polar spaces, generalised polygons,
buildings, partial geometries and their generalisations, special
subsets in Galois spaces with their translations in terms of codes.
*Dynamical Systems*
studies continuation and bifurcation of periodic and relatively
periodic solutions in reversible Hamiltonian systems.
- The arithmetical research of
*Algebra—Number Theory—Algebraic
Geometry* is focused on quadratic forms and division algebras
over local function fields (as part of an European
*Research Training Network* on K-theory and algebraic groups),
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 (part of the FWO-research project `Algebraic geometry, birational and
cohomological aspects', in collaboration with KULeuven).
*Infinitesimal Mathematics and Constructive Approximation* considers
infinitesimal refinements of geometry and analysis, applied to
foundations (such as Elementary Recursive Nonstandard Analysis, a
partial implementation of Hilberts programme) and to
constructive approximations of infinite order for generalised functions
and generalised derivability.
*Computer assisted Proving* develops a methodology
for specification and verification of soft-and hardware systems,
with computer implemented assistance for the underlying proofs.