Bar-Ilan Combinatorics Seminar (joint with the Mathematics Colloquium) (when) Sunday, 26 Tevet (Jan. 2), 12:00-13:00 *NOTE SPECIAL TIME* (where) Room 201 (Math Department Seminar Room), Math and CS Building (216), Bar-Ilan University (who) Nathan Keller (Weizmann Institute of Science) (what) "Discrete harmonic analysis of Boolean functions and its applications" Abstract: Boolean functions are a central object of study in combinatorics, complexity theory, probability theory and other areas of mathematics and computer science. In a paper from 1988, Kahn, Kalai and Linial (KKL) introduced the use of tools from harmonic analysis in the study of Boolean functions. The paper of KKL was the starting point of an entire area of research. In the last two decades the results of KKL were greatly expanded, the analytic tools were developed significantly, and the techniques were applied in numerous fields, including percolation theory, learning theory, social choice theory, etc. In this talk we will present the basic objects of study (e.g., influences, Fourier-Walsh expansion etc.) and the basic analytic tools (e.g. hypercontractive inequalities), and then we will show several new applications, focusing on applications to correlation inequalities, percolation theory, and social choice theory. Some of the results are based on joint works with Guy Kindler, and with Ehud Friedgut, Gil Kalai, and Noam Nisan. ************************************************************************* You are all invited! (Graduate students especially welcome) Seminar organizer: Ron Adin <radin@math.biu.ac.il> Seminar's homepage: <http://www.math.biu.ac.il/~radin/comsem/comsem.html> ************************************************************************* --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Ron Adin <radin@math.biu.ac.il>