Gunther Cornelissen
Study of the divisor of Eisenstein series related to supersingularity. Algebraic relations between torsion points of elliptic curves. Drinfeld modules and the algebraic structure of rings of modular forms.
Frank De Clerck
Constructions and characterizations of finite incidence structures and their adjacency graphs, with the emphasis on (semi)partial geometries and generalized quadrangles. Spreads of (semi)partial geometries. Distance regular graphs. Conical flocks.
Thomas De Smedt
-coverings 
of the projective line.
(Local case, and 
prime.)
Wim Mielants
Almost highly transitive permutation groups of countable degree.
Leo Storme
In 1995, my research was focussed on flocks and caps in projective spaces, and on the problem of the slopes of the graph of a function defined over a finite field.
Let 
be a quadratic cone in 
, q even,
with vertex 
and with base the conic 
in the plane 
. A flock of 
is a set
of q planes 
,
,
which intersect the set 
into
q disjoint conics.
The problem of classifying all flocks is still open. Different infinite classes and sporadic examples exist.
From February 18 till March 31, 1995, I visited the University of Western Australia (Perth, Australia) to work together with Prof. Dr. T. Penttila.
During this visit, we managed to classify all monomial flocks of 
. This means that we classified all flocks projectively
equivalent to a flock 
, 
.
Our results show that the only monomial flocks are:
(1) the linear flock: 
and 
with
irreducible over 
;
(2) the Fisher-Thas-Walker flock: 
and 
with q a non-square;
(3) the Payne flock: 
and 
with q a non-square.
These results will be published in the article, entitled: Monomial flocks and ovals.
Dr. A. Cossidente (University of Potenza, Italy) and myself looked for infinite classes of caps in
projective spaces. We managed to find two infinite classes of
- and 
-caps in 
. These caps have the
properties of being orbits of cyclic groups, and of being contained
in the intersection of parabolic quadrics.
The constructed infinite classes were then used to construct
infinite classes of 
-caps contained in the intersection
of hyperbolic quadrics in 
.
These results will be published in: Caps on parabolic and hyperbolic quadrics.
Prof. Dr. A. Blokhuis, Dr. S.M. Ball, Prof. Dr. A. Brouwer (Technical University of Eindhoven), Prof. Dr. T. Szonyi (Eötvös Loránd University, Budapest, Hungary), and myself studied the number of slopes of the graph of a function defined over a finite field.
Let 
and let 
be the set
of slopes defined by f.
To find information on |D|, consider the set 
so that |D| is the number of slopes of secants of U, and map
to 
.
If F is a subfield of L, then L is
a vector space over F, and a subset V of L will be
called F-linear if it is mapped in this way to a
F-subspace of L.
Then the following result was obtained:
Let 
be a point set of size q.
Let D be the set of slopes of secants of U, and put 
.
Let e (with 
) be the
largest integer such that each line with slope in D meets U in a
multiple of 
points. Then we have one of the following:
,
,
, e | n, and 
,
or 
and 
, then U is
a 
-linear subspace,
and all possibilities for N can be determined explicitly.
These results will be published in: On the number of slopes of
the graph of a function defined on a finite field.
Prof. Dr. J.W.P. Hirschfeld (University of Sussex, England) and myself
wrote in 1995 a survey article containing the most important results
on arcs, caps, (multiple) blocking sets, 
-arcs
in projective spaces.
The main results on these topics were gathered in a large number of tables to make these results easily accessible to anyone who needs these results.
The article The packing problem in statistics, coding theory, and finite projective spaces, containing these results, has been accepted for publication in the proceedings of the Bose Memorial Conference (Colorado, June 7-11, 1995) (J. Statist. Planning and Inference).
J. A. Thas
.
Jan Van Geel
Quadratic forms over function fields and conics. Description of the algebra of Drinfeld modular forms for artithmetic subgroups of the full modular group
GL
.
Hendrik Van Maldeghem
A characterization result for Moufang polygons:
every finite
2-Moufang polygon is a Moufang polygon. An analogue of Baer's theorem
for finite generalized polygons. A characterization of the infinite pappian
polygons over an algebraically closed field as the Moufang polygons of
finite Morley rank. Determination of weak embeddings of singular orthogonal,
symplectic and unitary polar spaces of non-singular rank at least three.
Characterizations of classes of finite generalized quadrangles by Veblen's
axiom. A coherent theory about folding buildings and unfolding apartments.
An elementary proof of Ott's result on polarities of finite generalized
hexagons. A construction of new ovoids and spreads in the finite generalized
hexagon 
.
Kristel Van Steen
Non-spherical (mainly affine) Tits-buildings of rank 3. By looking at automorphism groups, we give characterizations of some rank 3 affine buildings.
Karim Zahidi
Decision problems in number theory and algebraic geometry.