The Weizmann Institute of Science Faculty of Mathematics and Computer Science Mathematical Analysis and Applications Seminar Lecture Hall, Room 1, Ziskind Building on Tuesday, June 12, 2012 11:00 - noon Professor Michael Cwikel Technion will speak on A simple(?) geometric/combinatoric question with deep consequences for BMO functions Abstract: I will pose and invite you to solve a seemingly rather simple geometric/combinatoric question. So I hope that my audience will also include experts in combinatorics or high-dimensional discrete geometry, though no expertise in such domains will be assumed (or needed??). My coauthors and I have discovered that an affirmative answer to this question would have some very interesting consequences in analysis. They relate to the very important function space BMO (of functions of Bounded Mean Oscillation). I will briefly describe BMO, and mention some of its remarkable properties and connections with harmonic analysis and complex analysis. Special cases of one of our results give alternative proofs of the celebrated John-Nirenberg inequality for BMO functions. An affirmative answer to the above-mentioned question would lead to a version of the John-Nirenberg inequality with dimension free constants. A more extensive version of this abstract and a first version of our detailed paper etc. are available at <http://www.math.technion.ac.il/%7Emcwikel/bmo> This is joint work with Yoram Sagher and Pavel Shvartsman. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Yaeli Malka <yaeli.malka@weizmann.ac.il>