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, February 10, 2011 at 11:30 Note late start Ehud Friedgut Hebrew University will speak on Triangle-intersecting families of graphs Abstract: How many graphs can you choose on a fixed set of $n$ vertices such that the intersection of any two of them contains a triangle? S\'{o}s and Simonovits conjectured in 1976 that the largest such families of graphs are obtained by taking all graphs containing a fixed triangle, and that these are the only extremal constructions. This question turned out to be relatively resilient to the standard methods in extremal combinatorics, with partial progress being made in 1986 after Chung-Graham-Frankl-Shearer introduced some novel entropy arguments. Recently, with David Ellis and Yuval Filmus, we have been able to prove the conjecture, using discrete Fourier analysis and spectral methods. In this talk I'll sketch the proof. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Gady Kozma <gady.kozma@weizmann.ac.il>