Associate Professor,Department of Mathematics,University of Wisconsin, Madison Areas of interest: Topology of hypersurface singularities; Hyperplane arrangements;Intersection homology, Perverse Sheaves and applications to Singularities;Characteristic classes of singular spaces;Hodge Theory.
The intersection homology of Goresky-MacPherson is a homology theory well-suited for the study of singular spaces. I will first introduce intersection homology in the geometric way, i.e. using chains that meet the strata of a singular space in a controlled way, and I will prove the basic properties of this theory, e.g. that it satisfies Poincare Duality (while the usual homology does not). If time permits, I will also characterize the intersection (co)homology groups in terms of sheaves (using a description due to P. Deligne), and describe various applications to Singularity theory.