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Abstract:
(joint work with Assaf Naor) The Heisenberg group
H is a sub-Riemannian manifold that is hard to embed in
R^n. Cheeger and Kleiner introduced a new notion of
differentiation that they used to show that it does not embed nicely
into L_1. This notion is based on surfaces in H, and in
this talk, we will describe new techniques that let us quantify the
"roughness" of such surfaces, find sharp bounds on the distortion of
embeddings of H, and estimate the accuracy of an
approximate algorithm for the Sparsest Cut Problem.
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