The algebra of simplicial complexes.

Sara Faridi (UQÀM)

In this talk we associate to a simplicial complex a square-free monomial ideal called its "facet ideal". We use the combinatorial structure of a simplicial complex to study algebraic properties of its facet ideal. We explore dualities with Stanley-Reisner theory, and describe effective ways to compare the Stanley-Reisner complex to the facet complex for a given monomial ideal. As a result, we re-interpret some existing Cohen-Macaulay criteria, and produce some new ones.