This is an announcement for the paper "Neighborhoods on the Grasmannian of marginals with bounded isotropic constant" by Grigoris Paouris and Petros Valettas. Abstract: We show that for any isotropic log-concave probability measure $\mu$ on $\mathbb R^n$, for every $\varepsilon > 0$, every $1 \leq k \leq \sqrt{n}$ and any $E \in G_{n,k}$ there exists $F \in G_{n,k}$ with $d(E,F) < \varepsilon$ and $L_{\pi_F\mu} < C/\varepsilon$. Archive classification: math.FA Submitted from: petvalet@math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.4988 or http://arXiv.org/abs/1404.4988