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\centerline{\bf Description of the Bielefeld group} 
\centerline{\bf involved with the algebraic-combinatoric network}

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\centerline{Principal researcher:}
Prof.~Dr.~Andreas W.M. {\bf Dress}, full professor of mathematics
at Bielefeld University since 1969. Interests range from pure mathematics 
including e.g. representation and $K$-theory to very applied areas 
including e.g.
crystallography, chemistry, and  
computational biology: 
surprisingly often, activities in any one of these diverse fields have led
to developments which are closely related to questions studied in 
{\it algebraic combinatorics}.

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\centerline{Associated researchers (in alphabetical order):}

Dipl.math.~J\"orn {\bf Bornh\"oft}: in his diplom thesis, presented in 1994, 
he justified rigorously some computer-graphics procedures for drawing 
hyperbolic tilings, relying on the surprisingly close connection between these 
procedures and the word problem for discrete hyperbolic groups.

Dr.~Gunnar {\bf Brinkmann}: in his thesis, presented in 1991, he pioneered 
the first systematical approach towards a mathematical theory of local 
perturbations of periodic tilings, - a topic which simultaneously is 
very important in condensed matter physics and utterly neglected in 
mathematics.  Since then, he has not only broadened his approach; in addition,
he has established several world records through his computer programs for 
generating 
and enumerating all sorts of discrete structures (3-regular graphs, 
Fullerenes, hydrocarbon structures etc.).

Dr.~Olaf {\bf Delgado Friedrichs}: in his thesis, presented in 1994, 
he has worked out efficient 
algorithms concerning the 
construction and classification of periodic 3D-tilings, which have already 
been used successfully to solve systematically a number of 
problems in this field, which have not been attackable by any other 
known technique so far.

Dr.~Daniel {\bf Huson}: in his thesis, presented in 1990 and awarded with
a university price, he has developed computer algebra tools 
to generate and enumerate periodic 2D-tilings. 
In the last five years, he worked out
several refinements and
generalizations which, 
in the meantime, won international acclaim. He is now
- in cooperation with Olaf Delgado Friedrichs - extending his methods to the 
3D-case, while simultaneously constructing efficient methods to compute 
Delone tilings for periodic discrete point systems (e.g. atoms in 
crystalls) and improving the scientific and 
artistic options available in his and 
O. Delgado Friedrich's 2D-computer graphics package {\tt RepTiles}. 

Dipl.Math.~Lars {\bf Lauer}: in his diplom thesis, he studied local 
irregularities in otherwise regular hexagonal tilings. He is now extending
his approach to spherical structures (e.g. Fullerenes) and structures
with a well defined boundary structure (e.g. PentHex Puzzles).

Dr.~Vincent {\bf Moulton}: In his thesis, presented in 1994 at Duke University,
V. Moulton studied vector braids. He is now extending this study to 
encompass all sorts of subspace arrangements. In addition, he has started to work
on the combinatorics of finite metric spaces, relevant in combinatorial 
group theory as well as in e.g. phylogenetic studies.

Dr.~Christian {\bf Siebeneicher}: Akademischer Rat at Bielefeld University 
since 1975.
Since he studied $\lambda$-ring structures of Burnside rings in his thesis 
from 
1972, he has - among other things - continuously worked on various aspects
of Burnside-ring theory, including the fascinating connection with the 
Witt-vector construction.
 
Dipl.Inf.~Jens {\bf Stoye}: After finishing his diplom thesis in theoretical informatics,
J.~Stoye joined our biocomputing group to work on sequence alignment algorithms.

Dr.~S\"oren {\bf Perrey}: in his thesis, presented in 1994, he has developed
deeper insights into the behavior of Chess programs and other 
computer programs playing 
two-person games. He now works in the biocomputing group, 
in particular on new algorithms for sequence comparison.

Dr.~Werner {\bf Terhalle}: in his thesis, presented in 1992 and awarded with
a university price, he has studied 
an intriguing connection between valuated matroids and 
affine buildings. He is now using this approach to develop a 
deeper understanding
of ({\bf R-}) trees, and possible higher-dimensional generalizations 
of such trees.

Dipl.Math.~Bernd {\bf Volkmer}: he works on (strongly deterministic!) cellular automata
which can be used to produce (pseudo)random numbers and, hence, to simulate 
efficiently diffusion processes,- an important aspect in many other simulation tasks.


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