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Title: Invertible Homogeneous Metric Spaces Speaker: David Freeman (University of Cincinnati Blue Ash College) Time: Friday, October 10, 2014 at 3:00 pm Place: MSB 109A Abstract: What geometric and/or analytic properties characterize Euclidean space? More precisely, what conditions are necessary and sufficient to imply that a given metric space can be mapped onto a Euclidean space with bi-Lipschitz distortion? In light of this question we consider the fact that Euclidean space is isometrically homogeneous and can be “inverted” by way of Moebius transformations. It turns out that metric generalizations of such homogeneity and invertibility can be used to characterize Euclidean space within certain classes of metric spaces. We will frame such characterizations of Euclidean space within the broader context of recent efforts to obtain geometric/analytic characterizations of the boundaries of canonical hyperbolic spaces. Hoping to see you, Iddo