Geometry
In joint work with A. Kasikova and D. Pasechnik the classification of
multiple extensions of generalized hexagons related to groups in the Suzuki and McLaughlin chain has been completed.
This has lead to a purely combinatorial characterization of some geometries
related to the sporadic groups HJ, Suz, McL and 
.
Also affine extensions of generalized hexagons have been
studied in joint work with J. van Bon.
The investigation of extensions of generalized octagons has been started.
Regular line systems where two lines make an angle 
with 
or 
and their connection with lattices
have been investigated.
A paper on the classification of regular quaternionic polytopes has been written.
In joint work with H. Van Maldeghem and J. van Bon
a theory of hyperbolic lines in generalized polygons has been developed.
This has led to a characterization of the generalized hexagons
of type 
.
Some consequences of these results for embeddings of generalized polygons in projective spaces have been investigated.
Also embeddings of the geometries 
and 
into projective spaces have been studied.
For some geometries the dimension of the universal embedding space has been determined.
In joint work with A. Sali all perfect sum sets in Abelian groups have been determined.
The admissible partitions of 
, 
and 
have been determined.
More progress has been made in the theory of blocking sets in finite Desarguesian planes. Results obtained in joint work with S. Ball and T. Szönyi on multiple blocking sets, however, have been improved by very recent joint work (1995) with L. Storme and T. Szönyi.
It has been shown that there are no line spreads in 
consisting of only lines that are tangent to an elliptic quadric.
This result will probably be part of more extensive work together
with N. Hamilton.
In joint work with A.A. Bruen and D. Wehlau blocking caps have been investigated.
The computer game `Button Madness' has been analyzed. The sizes of the playground for which there is always a winning strategy have been determined up to 1000000.
A class of degenerations of 
surfaces of degree 6 has been studied in terms of lattices.
Graph Theory and Combinatorics
Together with T. Kloks it has been proved that the determination of the equivalence covering number for split graphs is NP-hard.
In joint work of I. Kaplansky, B.D. McKay and J.J. Seidel,
the problem of finding the maximal determinant of the matrices
of odd order with zeros on the main diagonal and 
else
has been studied.
Together with R. Wilson the p-rank of certain matrices related to symmetric groups has been investigated.
Together with M. Mulder it has been proved that for 
-graphs
the connectedness number equals the valency.
Some root graphs have been investigated.
All distance regular graphs of valency 4 have been classified. The amount of information available trough the `distance regular graphs server' has been extended considerably.
Theory of Groups and Lie algebras
Integrality and arithmetic questions on representations of finite groups in algebraic groups have been investigated.
The orbit space of 
acting on a 16-dimensional vector space
over k,
for k a field of characteristic 3, has been determined.
In particular it has been proved that the number of orbits is finite.
The Lie algebras generated by extremal elements (special nilpotent elements of order 3) have been studied. In case there are at most 4 generators it has been established that the dimension of the Lie algebra is finite. The Lie algebras generated by 3 special elements have been classified.
A class of Lie algebras in even characteristic, discovered by Kaplansky, has been characterized by properties of a generating set of elements. These generating sets carry the structure of a cotriangular space.
For finite dimensional Lie algebras some algorithms for finding the nilpotent or solvable radical have been developed and implemented.
A first draft for a project on canonical bases, quantum groups and representations of Lie algebras has been made.
The setup for the interactive book project ACELA has been specified.