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4:00 pm Friday, April 25, 2014 Wolfe Lecture: Ultrametric skeletonsby Assaf Naor (Courant Institute of Mathematical Sciences, NYU) in HBH 227- Let (X,d) be a compact metric space, and let mu be a Borel probability measure on X. We will show that any such metric measure space (X,d,mu) admits an "ultrametric skeleton": a compact subset S of X on which the metric inherited from X is approximately an ultrametric, equipped with a probability measure nu supported on S such that the metric measure space (S,d,nu) mimics useful geometric properties of the initial space (X,d,mu). We will make this geometric picture precise, and explain a variety of applications of ultrametric skeletons in analysis, geometry, computer science, and probability theory.
Submitted by hassett@math.rice.edu |