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: David Ralston, Ben-Gurion University Title: Heavy Sets: Structure and Dimension Date: Monday, January 17 Time: 14:30 Place: Schreiber 309 Abstract: Given a measure preserving transformation on a space and a function of zero mean, the heavy set is the set of points whose ergodic sums remain nonnegative for all (forward) time. After discussing a few generic results, we will turn our attention to the specific setting where the transformation is an irrational circle rotation and the function is the characteristic function of the interval [0,1/2]. In this setting, we will show that the heavy set is almost-surely (with regard to the rotation parameter) the union of a perfect Cantor set of both Hausdorff and box dimension c, where c is some constant strictly between zero and one, together with countably many isolated points. ALSO, in this week's Mathematics Colloquium, Monday from 12:15 to 13:15 in Schreiber 006, Hugo Duminil-Copin will speak on "Discrete complex analysis and statistical physics". Abstract: Discrete harmonic and discrete holomorphic functions have been proved to be very useful in many domains of mathematics. Recently, they have been at the heart of the two dimensional statistical physics (for instance, through the works of Kenyon, Schramm, Smirnov and others...). We will present some of the connections between discrete complex analysis and statistical physics. In particular (it is a joint work with S. Smirnov), we will use discrete holomorphic functions to prove that the number a_n of self-avoiding walks of length n (starting at the origin) on the hexagonal lattice satisfies: a_n^{1/n} ----> sqrt(2 + sqrt(2)) when n tends to infinity. This confirms a conjecture made by Nienhuis in 1982. 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>