The algebra of simplicial complexes.

    Sara Faridi, UQAM

Abstract: 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.