# Lipschitz Maps From Spaces With Many Rectifiable Curves

 GEOMETRY/DYNAMICAL SYSTEMS SEMINAR Topic: Lipschitz Maps From Spaces With Many Rectifiable Curves Speaker: Jeff Cheeger Affiliation: Courant Institute Date: Tuesday, February 23 Time/Room: 4:00pm - 5:00pm/S-101

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.