Tel Aviv University
Dear all,
Hope the passover vacation went well. This week at the Horowitz
seminar on Probability, Ergodic Theory and Dynamical Systems at Tel
Aviv University we are happy to have
Speaker: Ronen Eldan, Weizmann Institute
Title: On the connection between the spectral gap of convex bodies
       and the variance conjecture
Date: Monday, April 8
Time: 14:30
Place: Schreiber 309
We consider the uniform measure over a high-dimensional isotropic
convex body. We prove that, up to logarithmic factors, the
isoperimetric minimizers are ellipsoids. Equivalently, we show that
up to a logarithmic factor, the "worst-behaving" functions in the
corresponding poincare inequality are quadratic functions. We thus
establish a connection between two well-known conjectures regarding
the uniform measure over a high dimensional convex body, namely the
Thin-Shell conjecture and the conjecture by Kannan-Lovasz-Simonovits
(KLS), showing that a positive answer to the former will imply a
positive answer to the latter (up to a logarithmic factor). Our proof
relies on the analysis of the eigenvalues of a certain
random-matrix-valued stochastic process related to a convex body.
Best regards,
Seminar webpage:
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
Announcement from: Ron Peled   <>