Title: Hochster's formula for local cohomology, part 1

Abstract: A Stanley-Reisner ring is a quotient of a polynomial ring by an ideal generated by square-free monomials; these rings are in bijective correspondence with simplicial complexes, and there is a profound relationship between the algebraic properties of the ring and the topology of the simplicial complex. Hochster's formula for local cohomology is one of many famous theorems built on this relationship. In this week's talk, we will examine the mechanisms underlying Hochster's formula. Next week, we will introduce the notion of a "t-Stanley-Reisner ring" and adapt Hochster's formula to this new setting (joint work with Mel Hochster).