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Dear all, Hope to see you, Iddo. -- Title: Tangents and Local Set Approximation Speaker: Matthew Badger (University of Connecticut) Time: Friday, September 26, 2014 at 3:30 pm Place: MSB 109A Abstract: One way to interpret derivatives that we teach to our calculus students is that a derivative m=f′(x) exists exactly when `zooming in' on the graph of the function at (x,f(x)) transforms the graph into a tangent line with slope m. When graphs of differentiable functions are replaced by arbitrary closed sets in Euclidean space, there is a similar story: `zooming in' on a closed set along a sequence of scales produces a `tangent set'. In the first part of the talk, I will describe a nice topology on the space of nonempty closed subsets of Euclidean space that lets us make a rigorous definition of tangent sets. (For geometers: tangent sets are distinct from, but related to Gromov-Hausdorff limits of pointed metric spaces.) In the second part of the talk, I will discuss some recent applications of tangent sets to problems in geometric measure theory and partial differential equations. This is joint work with Stephen Lewis, who recently finished his PhD at the University of Washington and is now a postdoc at the University of Minnesota. I will try to make the talk accessible to graduate students and faculty who are interested in analysis and nearby fields.