Tel Aviv University Hello everyone, The next colloquium talk will be held on Monday,16/5/2011, 12:15, Schreiber 006, Tel Aviv University. The speaker is Emanuel Milman (Technion) and the title of his talk is Isoperimetric and Concentration Inequalities - Equivalence and Applications The abstract is given below. Tea and coffee at 12:00, same room. Hope to see you there. For information about future colloquiua, see <http://www.math.tau.ac.il/~klartagb/colloq_2010.html> You are all welcome to suggest colloquium speakers for the next academic year. Yours, Bo'az ------------------------- Abstract: Given a metric space equipped with a measure, various ways exist for studying the interaction between measure and metric. A very strong form is given by isoperimetric inequalities, which for a set of given measure, provide a lower bound on its boundary measure. A much weaker form is given by concentration inequalities, which quantify large-deviation behavior of measures of separated sets. There are also other tiers, interpolating between these two extremes, such as the tier of Sobolev-type inequalities. It is classical that isoperimetric inequalities imply corresponding functional versions, which in turn imply concentration counterparts, but in general, these implications cannot be reversed. We show that under a suitable (possibly negative) lower bound on the generalized Ricci curvature of a Riemannian-manifold-with-density, completely general concentration inequalities imply back their isoperimetric counterparts, up to dimension independent bounds. Consequently, in such spaces, all of the above tiers of the hierarchy are equivalent. Time permitting, we will mention several applications of this result, ranging from Statistical Mechanics to Spectral Geometry. We also derive new sharp isoperimetric inequalities, generalizing classical results due to P. Levy, Sudakov-Tsirelson and Borell, Gromov and Bakry-Ledoux, into one single form. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Bo'az Klartag <klartagb@post.tau.ac.il>