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Wednesday, November 9, 2005

**Abstract:** We will begin with a review of some (co)homology theories like singular, simplicial, sheaf etc and some theorems like Poincare Duality valid for nonsingular spaces. By considering some examples we will see how these theorems fail to hold if the space has singularities. Intersection (co)homology (IC) provides a setting where these theorems are true even for spaces with singularities. We will conclude with a discussion of sheaf theoretic versions of IC and perverse sheaves. The talk should be of interest to survivors of courses like Algebraic Topology or any version of Algebraic Geometry.