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Thursday, November 3, 2016

**Abstract:** In the 1950's John Nash famously proved that every Riemannian manifold admits an isometric embedding into Euclidean space. In this talk I will explain Nash's results and discuss adaptations of his isometric embedding theorem(s) to other types of spaces. These spaces include various types of manifolds, polyhedra, and more generally length metric spaces. This talk will mostly be a "state of the art" survey on what is known about the isometric embedding problem for the spaces listed above.