Mathematics Colloquia and Seminars
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Grobner bases of Point ConfigurationsAlgebra & Discrete Mathematics
|Speaker: ||Prof. Shmuel Onn, Technion- Haifa Israel and UC Davis|
|Location: ||593 Kerr|
|Start time: ||Tue, Oct 9 2001, 10:00AM|
In this talk I'll overview work joint with Bernd Sturmfels where
we construct the State Polyhedron of any configuration of finitely
many points in affine space. Its vertices then stand in bijection
with the various reduced Grobner bases of the point configuration.
Combining our characterization of all the reduced Groebner bases
of a point configuration with a polynomial time procedure for
enumerating the vertices of the State Polyhedron, we are able to
provide a polynomial time algorithm for computing the Universal
Grobner basis of the generic configuration in any fixed dimension.
The talk will be self contained and is intended to provide a quick
introduction to Grobner bases, Grobner fans and State polyhedra of
polynomial ideals. I will mention some questions related to the
non-generic case, as well as enumerative questions regarding improved
bounds (I'll describe the recent best-so-far ones by Wagner and Remond).