Intersection Homology and Combinatorics

This is a draft lecture notes written under my guidance for today’s lecture. Blue text represent my further comments.) The lecture will be on Oct 7 at IAS, at 3:30, in the Seminar room. I will speak at the IAS about the wonderful theory of intersection homology, introduced by Mark Goresky and Bob MacPherson, and some of its connections to combinatorics. This post is an extended description of the lecture and a set of notes toward it. I would like to explain the basic definitions, then discuss three directions that particularly interest me: the missing ring structure behind toric -vectors, the search for intersection homology in face rings, and extensions involving several perversities. These questions continue discussions from the pleasant informal seminar we had here in 1995 with Bob MacPherson, Mark Goresky, Tom Braden, and a few others. I will try to keep the discussion self-contained and easygoing. Throughout, coefficients are rational unless another field is specified. I will…