#
Monday Lecture and Colloquium

**November 27, 2006**

Freie Universität Berlin

Institut für Informatik

Takustr. 9, 14195 Berlin

room 005

** Lecture - 14:15**

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Volkmar Welker - Universität Marburg

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Barycentric Subdivisions (joint work with Francesco Brenti)

*Abstract:*

We study barycentric subdivisions of simplicial complexes and
more generally of (compact) polytopal complexes. We are interested
in the behavior of the F-vector and h-vector of the complex under
single and iterated subdivision. Recall that the components f_i
of the f-vector count the number of i-dimensional simplices (resp.
polytopes) in the complex.

We will give a series of results on the transformation of the
f-vector and h-vector under subdivision and the behavior of the roots of
the generating polynomial of the f-vector under subdivision.
We study simplicial complexes and cubical complexes and complexes
that arise by standard construction from polytope theory.

**Colloquium - 16:00**

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Christian Haase - Freie Universität Berlin

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Who is afraid of Toric Algebra?

*Abstract:*

Statements like "*The proof of the g-Theorem for convex
polytopes involves the Hard Lefschetz Theorem for projective toric
varieties.*" provoke a light sense of anguish in many a
combinatorialist.
This fear is unjustified. In this talk, I want to explain the simple
mechanism how toric algebra translates combinatorial problems into
algebraic ones (and vice versa). And I want to give examples where
it worked.

Letzte Aktualisierung:
20.11.2006