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In-Person TalkÌý

In this talk I will give a broad overview of correlation inequalities for linear extensions of finite posets.ÌýI will start by reviewing theÌýbackground: Stanley's log-concave inequality, Shepp's XYZ inequality, etc. I will then proceed to describe two new families of correlation inequalities which we recently established.Ìý The first is motivated by the Huh–Schröter–Wang correlation inequalities for matroids, and is proved via the technology of combinatorial atlases.Ìý The second is motivated by the Lam–Pylyavskyy inequalities for Schur functions, and is proved via the multivariate generalization of the Ahlswede–Daykin inequality.Ìý

This is joint workÌýwith Swee Hong Chan.ÌýÌý