Columbia Mathematics Department Colloquium

 Ultrametric skeletons


Assaf Naor

Courant Institute, NYU



           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.

Joint work with Manor Mendel.


Wednesday, February 15th, 5:00 - 6:00 p.m.
Mathematics 520
Tea will be served at 4:30 p.m.