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.
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Bo'az Klartag   <klartagb@post.tau.ac.il>