Tel Aviv University Dear all, Following the passover break, the Horowitz seminar renews its activity this Monday with a talk by Mikhail Sodin. NOTE THE SPECIAL END TIME! The talk will be longer than usual. Speaker: Mikhail Sodin, Tel Aviv University Title: Random nodal portraits Date: Monday, April 16 Time: from 14:30 to 16:00! Place: Schreiber 309 Abstract: We describe the progress in understanding the zero sets of smooth Gaussian random functions of several real variables. The primary examples are various ensembles of Gaussian real-valued polynomials (algebraic or trigonometric) of large degree, and smooth Gaussian functions on the Euclidean space with translation-invariant distribution. The fundamental question is the one on the asymptotic behaviour of the number of connected components of the zero set. This can be viewed as a statistical version of Hilbert's 16th problem. We start with an intriguing heuristics suggested by Bogomolny and Schmit, which relates nodal portraits of 2D Gaussian monochromatic waves to bond percolation on the square lattice. Then we explain how Ergodic Theorem and rudimentary harmonic analysis help to find the order of growth of the typical number of connected components of the zero set. We will mention a number of basic questions, which remain widely open. The talk is based on joint works with Fedor Nazarov. 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@gmail.com>