November 27, 2006
Freie Universität Berlin
Institut für Informatik
Takustr. 9, 14195 Berlin
room 005
Lecture - 14:15
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
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.