Tel Aviv University Dear all, This week at the Horowitz seminar on Probability, Ergodic Theory and Dynamical Systems at Tel Aviv University we are happy to have: Speaker: Elchanan Mossel, University of California, Berkeley Title: Robust Optimality of Gaussian Noise Stability Date: Monday, June 17 Time: 14:30 Place: Schreiber 309 Abstract: In 1985 C. Borell proved that under the Gaussian measure, half-spaces are the most stable sets. I will present two new proofs of this result. The first proof solves a long standing open problem by showing that half-spaces are the unique optimizers. It also provides quantitative dimension independent versions of uniqueness, showing that a set which is almost optimally noise stable must be close to a half-space. This has a number of application in theoretical computer science and social choice. The first proof also allows to answer a long standing open problem by Ledoux. The second proof is proved by induction on dimension in the discrete cube which allows to derive a proof of "Majority is Stablest" in the "Sum of Squares Proof System" thus aswering a recent question regarding semi-definite relaxations. Based on joint works with J. Neeman and Anindya De. 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>