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Boundaries of spaces of non-positive curvature

Abstract: Boundaries of hyperbolic spaces play an important role in the study of hyperbolic groups. Analogous boundaries exist for simply connected spaces of nonpositive curvature (CAT(0) spaces) but they are not as well behaved and hence less effective. I will review the differences between these two settings and then talk about work on a new boundary for CAT(0) spaces designed to isolate hyperbolic-like behavior in the usual boundary.