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Lectures and Colloquia during the semester



July 11, 2005

Freie Universität Berlin - Institut für Informatik
Takustraße 9
14195 Berlin
Room 005           - map -
Lecture - 14:15

Ralph-Hardo Schulz -Freie Universität Berlin

Translation groups in design theory

Abstract: On affine spaces and on desarguesian affine planes, the full translation group operates transitively and fixed point freely. This fact permits a representation of the geometry inside this group and an application of group properties to the geometry. A similar recipe can be applied as well to the theory of divisible designs.

Here, a finite incidence structure D with ``point set'' P und ``block set'' D ⊆ $P \choose k$ is called an ``(s,k,λ)-(group) divisible design'' if P can be partitioned into classes of equal size s such that any two points of different classes lie together in exactly λ blocks and two points in the same class have no common block. Examples are the finite affine planes and spaces and other 2-designs (that are divisible designs with s=1).

To each such design, there corresponds a constant weight code, so there is an application to these codes, too.

After a short historic introduction, we investigate divisible designs admitting a transitive translation group. Only three types of such groups can occur. Vice versa, this description allows the construction of many series of such designs.

A method of A.G.Spera to construct divisible designs needs certain transitivities of permutation groups. Many of these groups use the properties of translation groups and 2-transitive groups of affine spaces and planes. Other examples come from 3-transitive groups operating on the points of Laguerre geometries.

A generalization is a method of S.Giese to construct divisible designs by embedding designs in projective hyperplanes and using, as before, the translation group of the affine space. The designs gained in such a way allow a ``full dual translation group'' which, on the other hand, can be used to characterize a class of divisible designs as substructures of affine spaces.


Colloquium - 16:00

Kevin Buchin - Freie Universität Berlin

The Flow Complex: General Structure and Algorithm

Abstract: The flow complex is a data structure, similar to the Delaunay triangulation, to organize a set of possibly weighted points in Rd. Its structure has been examined in detail in two and three dimensions but only little is known about its structure in general. We present an algorithm for computing the flow complex in any dimension which reflects its recursive structure. On the basis of the algorithm we give a generalized proof of the homotopy equivalence of alpha- and flow-shapes. This is joint work with Joachim Giesen.


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