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2014 Wolfe Lecture in Mathematics

Dr. Assaf Naor
Courant Institute for Mathematical Sciences

New York University


Friday April 25, 2014
4:00pm, Herman Brown 227


Title: Ultrametric skeletons

 

Abstract: 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.

 

 

The Annual Wolfe Lectures are supported through a generous gift from the estate of Raquel A. Wolfe in loving memory of her husband, Dr. Alfred S. Wolfe, and his love for math which he instilled in both his children.

 

Updated July 1, 2014