Tel Aviv University Hello everyone, The next colloquium talk will be held on: Monday, 3/12/2012, 12:15, Schreiber 006, Tel Aviv University. Speaker: Wojciech Samotij (University of Cambridge and Tel Aviv University) Title: Independent sets in hypergraphs. 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: Many important theorems and conjectures in combinatorics, such as the theorem of Szemeredi on arithmetic progressions and the Erdos-Stone Theorem in extremal graph theory, can be phrased as statements about families of independent sets in certain uniform hypergraphs. In recent years, an important trend in extremal and probabilistic combinatorics has been to extend such classical results to the so-called `sparse random setting'. This line of research has recently culminated in the breakthroughs of Conlon and Gowers and of Schacht, who developed general tools for solving problems of this type. Although these two approaches solved very similar sets of longstanding open problems, the methods used are very different from one another and have different strengths and weaknesses. In the talk, we describe a third, completely different approach to proving extremal and structural results in sparse random sets that also yields their natural `counting' counterparts. We give a structural characterization of the independent sets in a large class of uniform hypergraphs by showing that every independent set is almost contained in one of a small number of relatively sparse sets. We then show how to derive many interesting results as fairly straightforward consequences of this abstract theorem. Based on joint work with Jozsef Balogh and Robert Morris. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: <ostrover@post.tau.ac.il>