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Tuesday, October 8, 2013

**Abstract:** I will discuss the Hodge cohomology and a refinement of the intersection homology of stratified spaces. Because of the singularities of the space, Hodge cohomology requires imposing `ideal boundary conditions', which depend on a consistent system of flat vector bundles over the singular set. On the other hand this system can be used to define a sheaf `refining' the sheaves of middle perversity intersection homology. The resulting cohomology theories coincide. This is joint work with Eric Leichtnam, Paolo Piazza, Rafe Mazzeo, and Markus Banagl.