This is an announcement for the paper "Trees and Markov convexity" by James R. Lee, Assaf Naor, and Yuval Peres. Abstract: We show that an infinite weighted tree admits a bi-Lipschitz embedding into Hilbert space if and only if it does not contain arbitrarily large complete binary trees with uniformly bounded distortion. We also introduce a new metric invariant called Markov convexity, and show how it can be used to compute the Euclidean distortion of any metric tree up to universal factors. Archive classification: math.MG math.FA The source file(s), TreeMarkov-GAFA.tex: 228845 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0706.0545 or http://arXiv.org/abs/0706.0545 or by email in unzipped form by transmitting an empty message with subject line uget 0706.0545 or in gzipped form by using subject line get 0706.0545 to: math@arXiv.org.