Mardi 20 Novembre 2007, 14h, Salle S16 (Passage Saumon niveau -1)
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Orateur/Speaker :
Jürgen Bokowski, TU Darmstadt
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Titre/Title :
Oriented matroids, i.e., a natural extended equivalence class of matrices,
with applications to polyhedral embeddings and point line configurations
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Résumé/Abstract :
We can interpret an (nxr)-matrix with non-zero row vectors
as an ordered set of oriented central hyperplanes. It is very natural to
consider
the equivalence class of all (nxr)-matrices that define a rotated image
of the given set of oriented hyperplanes. When we think of the (oriented)
great spheres that are defined by these oriented hyperplanes on the unit
sphere
and its induced cell decomposition on the unit sphere, we are often
interested in
the topological structure alone. In other words, we study topological
cell decompositions and we are interested in an invariant description of
such a
cell decomposition that is not only invariant with respect to central
rotations
but that is also invariant under more general topological transformations of
the
unit sphere. The resulting corresponding concept is that of an oriented
matroid.
After an introduction of this general concept, we discuss problems from
polyhedral
embeddings and that of point line configurations just as the peak of an
iceberg
for applications of the theory of oriented matroids. A decisive property of
an oriented
matroid is that it can also be naturally described by a finite set of signs.
The talk discusses the use of functional programming (Haskell)
in the context of oriented matroids, too.