Graduiertenkolleg: Methods for Discrete Structures

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Monday Lecture and Colloquium

November 27, 2006

Freie Universität Berlin
Institut für Informatik
Takustr. 9, 14195 Berlin
room 005

Lecture - 14:15

Volkmar Welker - Universität Marburg

Barycentric Subdivisions (joint work with Francesco Brenti)

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

Christian Haase - Freie Universität Berlin

Who is afraid of Toric Algebra?

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