## 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.