University of Haifa Mathematics Colloquium On Tuesday, April 24, 2012 at 16:10 in room 570 of the Science & Educ. Bldg, (note the special room) Elon Lindenstrauss, Hebrew University will speak on Homogeneous Dynamics and Diagonalizable Actions Abstract: Algebraic actions on quotient spaces of a group G by a discrete subgroup Gamma give highly interesting dynamical systems that are in many cases intimately linked with number theory. One of the most powerful ways to study these dynamical systems is to study the collection of invariant probability measures. Such a study forms the core of Ratner's landmark proof of the Raghunathan conjecture regarding orbits of unipotent groups. Already in the 1950's Cassels and Swinnerton Dyer observed (in a dual language) that higher rank diagonal groups have interesting rigidity properties which are still far from being understood. I will survey the progress made in this direction, particularly regarding the measure classification question, as well as the challenges that remain. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Oren Ben-Bassat <ben-bassat@math.haifa.ac.il>