[Banach] Abstract of a paper by Sean Li and Assaf Naor

This is an announcement for the paper "Discretization and affine approximation in high dimensions" by Sean Li and Assaf Naor. Abstract: Lower estimates are obtained for the macroscopic scale of affine approximability of vector-valued Lipschitz functions on finite dimensional normed spaces, completing the work of Bates, Johnson, Lindenstrass, Preiss and Schechtman. This yields a new approach to Bourgain's discretization theorem for superreflexive targets. Archive classification: math.FA math.MG Submitted from: naor@cims.nyu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1202.2567 or http://arXiv.org/abs/1202.2567