Abstract:

We will give an overview of work during roughly the past 10 years on the subject in the title. Some of this is joint with B. Kleiner and with Kleiner and A. Naor. We hope to cover differentiability of real valued Lipschitz functions, Banach space targets with the Radon-Nikodym-Property, the Carnot-Caratheodory/Heisenberg example, quantitative bi-Lipschitz nonembedding for Heisenberg in L_1 and applications to the worst case performance of the Goemans-Linial algorithm for the sparest cut problem with general demands.