PURE DEPARTMENT SEMINAR:

Speaker: Dr. Anthony Henderson (University of Sydney)

Title: Poset homology and the cohomology of real DeConcini-Procesi models

Date: Tuesday, 15 August 2006
Time: 2:00 pm
Venue: RC-4082, The Red Centre, UNSW

Let A be a finite collection of subspaces in a real vector space V.
A beautiful result of Goresky and MacPherson describes the cohomology
of the complement V - A in purely combinatorial terms, using the
homology of the poset of intersections of elements of A. (This
generalizes the work of Orlik and Solomon on complex hyperplane arrangements.)
A striking analogue, discovered recently by Eric Rains, describes the
cohomology of the associated DeConcini-Procesi model, a smooth compact real
variety. I will discuss and compare these two results, and present a new
generating-function formula for the Betti numbers of the real DeConcini-Procesi
variety of type B.