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 Abstract: 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, Ron Seminar webpage: <http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Ron Peled <peledron@post.tau.ac.il>