January 20, 2010
Kathrin Vorwerk (KTH): The Grassmannian and the associahedron
Abstract:
In this talk, I will present the result of recent joint work with
Martina Kubitzke. We begin with a review of Grassmann-Plücker
ideals and how they are related to the Hibi rings of certain posets as
well as unimodular triangulations of their order polytopes. We then construct an initial ideal for the Grassmann-Plücker ideal of
planes in n-dimensional space that is the Stanley-Reisner ideal of the
join of a simplex and the simplicial associahedron. For that, we use a
special case of reverse lexicographic triangulations as introduced by
Athanasiadis. Finally, we discuss the case of Grassmann-Plücker ideals of
higher-dimensional subspaces where analogous results are still to be found.