Tel Aviv University Hello everyone, The next colloquium talk will be held on: Monday, 18/3/2012, 12:15, Schreiber 006, Tel Aviv University. Speaker: Dan Romik (University of California, Davis) Title: Random noncrossing matchings arising in percolation theory. The abstract is given below. Tea and coffee at 12:00, same room. Hope to see you there. For information about future colloquia, see <http://www.math.tau.ac.il/~ostrover/colloquium/colloq2012.html> Yours, Yaron ******************************************************* Abstract: In probability theory and statistical physics, bond percolation on the square lattice is a natural model for a porous random medium and provides one of the simplest examples of a phase transition. At criticality, it has remarkable long-range correlation properties (many of them still conjectural). This talk will focus on "connectivity patterns" associated with a percolation configuration, which are random noncrossing matchings of the integers that encode connectivity information. Mysteriously, the probabilities for interesting events on connectivity patterns are dyadic rational numbers such as 3/8, 59/1024 and 69693/2^21. This "rationality phenomenon" can be proved in a few cases but remains mostly conjectural. I will describe the background and history of the model as well as new results that shed light on the problem by reducing the proof of the rationality phenomenon to a family of purely algebraic identities about coefficients of certain multivariate polynomials. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: <ostrover@post.tau.ac.il>