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