Alan Huckleberry

The goal of the talk is to explain complex geometric phenomena which have been of basic use in recent work giving computable descriptions of certain domains which arise in transforming cohomology to the level of fuctions in a context of representation theoretic interest. Incidence geometry arises as a tool for computing integrals over high-dimensional sets by intersecting with classically defined transversal varieties. Proper understanding of this incidence geometry also leads to proof of the hyperbolicity and complex geometric convexity of these domains. The exact determination of the domains then results from a study of analytic continuation in a concrete low-dimensional situation.