Bennet Goeckner

Simplicial complexes arise naturally in many areas of mathematics. They can be used to model topological spaces, they correspond to square-free monomial ideals of polynomial rings, and certain simplicial complexes generalize the notion of linear independence. Many properties of simplicial complexes can be defined equivalently via either combinatorics, topology, or algebra, and much work has been done to understand how properties from these three areas interact in this setting. This talk will start by surveying some representative results from this area. We will also resolve a conjecture of Stanley on decompositions of simplicial complexes that possess a property that generalizes acyclicity (based on joint work with Joseph Doolittle). No specific knowledge on these subjects will be assumed.