TEL AVIV UNIVERSITY Hello everyone, The next colloquium talk will be held on: Monday, 12/11/2012, 12:15, Schreiber 006, Tel Aviv University. Speaker: Amos Nevo (Technion) Title: Diophantine approximation, arithmetic groups, and ergodic 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: One of the main goals of classical metric Diophantine approximation is to quantify the denseness of the rational numbers in the real numbers, or more generally, of Q^d in R^d. An equally natural problem is to quantify the denseness of the rational points on the sphere, and more generally, rational points in other compact and non-compact algebraic sub-varieties in R^d. We will describe a solution to this problem for a large class of homogeneous varieties. The method we use is based on a general quantitative duality principle in homogeneous dynamics that we develop, and on spectral estimates of ergodic averages using the theory of automorphic forms. Based on joint work with Alex Gorodnik, and on joint work with Anish Ghosh and Alex Gorodnik. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: <ostrover@post.tau.ac.il>