This is an announcement for the paper "Sparse quadratic forms and their geometric applications (after Batson, Spielman and Srivastava)" by Assaf Naor. Abstract: We survey the work of Batson, Spielman and Srivastava on graph sparsification, and we describe some of its recently discovered geometric applications. Archive classification: math.FA Remarks: appeared as s\'eminaire Bourbaki expos\'e no. 1033, 2011 Submitted from: naor@cims.nyu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1101.4324 or http://arXiv.org/abs/1101.4324