Title: What is Intersection Homology?
Speaker: Chris Elliott
Speaker Info: 2nd Year
The theory of singular homology and cohomology of manifolds is a powerful tool in understanding the topology of smooth spaces, such as smooth algebraic varieties over the complex numbers. But what if -- as is often the case in algebraic geometry -- the spaces we want to consider typically have singularities? In this case foundational theorems such as Poincare duality no longer hold. In my talk I will explain the concept of Intersection Homology, as originally introduced by Goresky and Macpherson to deal with precisely this situation. This is a kind of homology theory for spaces with singularities in which one can recover many of the nice results that are true of homology of smooth manifolds. I will assume no knowledge of topology or algebraic geometry beyond basic notions of singular homology.Date: Tuesday, October 18, 2011