Geometry/Dynamical Systems Seminar

We will survey results (partly joint with Kleiner, and with Kleiner and Naor) on possibly fractal metric spaces which in a suitable sense have many rectifiable curves. We will try to cover: differentiable structure, a bi-Lipschitz nonembedding theorem for Banach space targets with the Radon-Nikodym Property, the example of Heisenberg group with its Carnot-Caratheodory metric, a quantitative bi-Lipschitz nonembedding theorem for the Heisenberg group in $L_1$ and an application to theoretical computer science.