Title:  Constructing Simplicial Spheres Using Algebra

Abstract:  Simplicial complexes are a central subject of study in combinatorics. They are also of interest geometrically since that abstract simplicial complex can be realized in real space as a geometric object. One interesting question is when is a simplicial complex homeomorphic to a sphere. We call these simplicial spheres. Using the connection of the Stanley-Reisner ring we can study simplicial complexes by looking at a corresponding ring. In particular the Gorenstein property occurs in these rings exactly when they are simplicial spheres. Hence we can construct simplicial spheres by constructing certain Gorenstein rings. This talk is meant to show the usefulness of the Stanley-Reisner ring connection between combinatorics and algebra and should be accessible to a general audience.

(Pizza at 4:00, talk at 4:15)