============================== Bar-Ilan Combinatorics Seminar ============================== The last meeting of the seminar this "semester" will take place, IYH, on (when) Tuesday, 1 Shvat (Jan. 8) refreshments at 11:45, talk at 12:00 noon (where) Room 331 (Math Dept Seminar Room), Math and CS Building (216), Bar-Ilan University (who) Nathan Keller (Hebrew University) will talk about (what) "On the correlation of monotone functions on the discrete cube" Abstract: --------- A well-known theorem of Kleitman (1966) asserts that every two monotone families of subsets of an $n$-elememt set are non-negatively correlated. Kleitman's result, along with numerous generalizations, are extremely useful in Combinatorics. In 1996, Talagrand improved Kleitman's theorem and established a lower bound on the correlation in terms of how much the characteristic functions of the monotone families depend simultaneously on the same variables. In this talk we discuss various generalizations of Talagrand's result, including generalizations to monotone non-Boolean functions on the discrete cube endowed with a general product measure, generalizations to functions on the continuous cube, generalizations to correlation of more than two families, and improved lower bounds on the correlation in the average case. The new results are achieved using analytic tools, mainly the Fourier-Walsh expansion of functions on the discrete cube and a hypercontractive inequality due to Bonamie and Beckner. ************************************************************************* You are all invited ! (Graduate students especially welcome) If you want to give a talk at the seminar, or know a prospective speaker, please contact Ron Adin . Seminar's homepage: see *************************************************************************