I. Bloemen:
Examination of translation ovoids of the classical generalized
quadrangles 
and 
in order to, under certain
conditions, classify them.
We also used the computer (and the language GAP) to say something
more in the case of small q.
Searching, with the use of a computer (and the language GAP), for
-caps K on 
which have the property that no 3
points are contained in a tangent plane of 
. Such a cap
defines a GQ
(see `Constructions of Polygons from Buildings' by E. E. Shult and J.
A. Thas.)
Characterizing the only known example (i.e. the one coming from the
elliptic quadric 
).
Dr. K. Coolsaet:
Interesting geometric substructures of the Ree-Tits octagon
of order 
and its dual.
G. Cornelissen:
Problems related to Drinfeld Modular Curves:
We investigate properties of the zeroes of Eisenstein
series for the action of 
on the
Drinfeld upper half plane : j-invariants, normalisation
of absolute value, ellipticity, transcendence, number of
zeroes in distinct orbits, vanishing order of the zeroes and
connection with invariants of supersingular reduction for
rank 2 
Drinfeld modules.
Secondly we investigate the generating problem for the algebra of modular forms for a principal congruence subgroup over the ring of functions on an algebraic curve over a finite field which are regular outside a given point : it is generated by its weight one and two part, and the weight one part is generated by Eisenstein series. We also look at the problem of finding relations between the generators.
Prof.dr. F. De Clerck:
Research interests are finite incidence structures
and their adjacency graphs, with the emphasis on partial geometries,
semipartial geometries and on generalized quadrangles.
Sometimes small computer programmes in GAP and MAGMA are written in order to
investigate characterizing properties of incidence structures with small
parameters. The goal here is to give a computer free proof.
This has been successful for the classification of the conical flocks in
PG(3,q), 
, and for constructing new examples, such as a non-linear
conical flock in PG(3,16) which afterwards turned out to be the
smallest example of the infinite class of Subiaco type.
T. De Smedt:
Endomorphism rings of Drinfeld-modules over finite fields
and their maximality as an order.
Some problems concerning compound matrices.
Prof.dr. W. Mielants:
Countable random models of first order theories. The existence
of residual orbits of the symmetry groups of such models.
Dr. L. Storme:
In 1994, my research was focussed
on flocks, arcs and caps in projective spaces.
Using a recently found relation between flocks of quadratic cones
in 
and arcs in 
, q even, a well-known
theorem by Segre on the extendability of arcs in 
, q even,
was used to extend partial flocks of quadratic cones in 
, q even.
Together with J.A. Thas, it was proved that large partial flocks
always can be extended to flocks. In this way, a previous result
by
Payne and Thas was improved considerably.
I also focussed on arcs in 
, q even, which are fixed by a
transitive projective group. Arcs fixed by a group
not stabilizing
a point, line or triangle, are characterized. This led to new arcs
in 
, q even square.
Together with F. Pambianco (university of Perugia (Italy)),
a construction of small complete caps in 
, q even, by Segre, was
generalized.
More precisely, complete 
-caps in 
,
q even, q>2,
and 
-caps in 
, q even, q>2, were
constructed.
The importance of these results lies in the fact that the caps in
have a size of the same order as the trivial lower bound
for the size of complete caps
in 
. Hence this lower bound is not that trivial. It gives
a clear indication for the size of the smallest complete cap in 
,
q even.
The research on caps was continued by showing the equivalence of
two constructions of 
-caps in 
by
Ebert and Kestenband. This extends results by Boros
and Szonyi who
had proved the equivalence in the planar case.
Prof.dr. J.A. Thas:
Embeddings of generalized hexagons in finite projective spaces. Weak embeddings of polar spaces in projective spaces. Constructions of polygons from buildings. Partial ovoids and partial spreads of polar spaces. m-systems and partial m-systems of polar spaces. Characterizations of finite classical generalized quadrangles. Flocks and partial flocks of cones in 
.
Prof.dr. J. Van Geel:
Quadratic forms over function fields of conics.
Description of the algebra of Drinfeld-Modular forms for arithmetic
subgroups
of the full modular group 
.
Prof.dr. H. Van Maldeghem:
Some new characterization results of Moufang polygons, in
particular a geometric characterization of the perfect Ree-Tits octagons;
a geometric construction of a certain class of twisted field planes by
means of Ree unitals; classification of ideal embeddings of finite
hexagons; determination of weak embeddings of non-singular orthogonal,
symplectic and unitary polar spaces of rank at least three and of finite
generalized quadrangles; a geometric characterization of the
Suzuki-Tits inversive planes; some results about infinite flocks of cones.
K. Van Steen:
Research of transitivity properties in affine triangle buildings.
K. Zahidi:
Decision problems in logic, extensions of Hilbert's Tenth Problem