A-graded methods for monomial ideals
  We use \ZZ^d-gradings to study d-dimensional monomial ideals. The Koszul functor is employed to interpret the quasidegrees of local cohomology in terms of the geometry of distractions and to explicitly compute the multiplicities of exponents. These multigraded techniques originate from the study of hypergeometric systems of differential equations. 
Christine Berkesch, Laura Felicia Matusevich