The Weizmann Institute of Science Faculty of Mathematics and Computer Science Geometric Functional Analysis and Probability Seminar Seminar Room, Room 261, Ziskind Building on Thursday, December 16, 2010 11:00 - 13:00 David Ralston Ben Gurion University will speak on Growth rates and one-sided boundedness of a particular ergodic sum Abstract: Using nothing more sophisticated than first-return maps and elementary properties of continued fractions, we will develop a constructive approach to studying the sequence of ergodic sums of the characteristic function of the interval $[0,1/2]$ under an irrational rotation of the circle minus the characteristic function of $(1/2,1)$, to ensure zero mean. The principle benefit of the elementary (but somewhat tedious) approach is that statements may be derived about specific rotations, as opposed to generic ones. Our primary topics of investigation will be: -What growth rates are allowed for such sequences? -What is the structure of the set of positions whose ergodic sums are always nonnegative? In both cases we will develop specific examples. Time permitting, we will then discuss applications of these techniques to informal questions of K. Park and W. Veech, as well as ongoing work regarding dynamics on a particular infinite translation surface (joint work with Barak Weiss of Ben Guiron University). --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Gady Kozma <gady.kozma@weizmann.ac.il>