In the past decades there was an explosion in the number of correlation inequalities, of which the FKG inequality is probably best known. While applications to Probability and Statistical Physics were the original motivations, many recent connections to matroid inequalities, Algebraic Combinatorics and Poset Theory brought additional interest to the subject. I will give an overview of some older results (Fishburn and Björner inequalities, Lam-Postnikov-Pylyavskyy inequalities) and some of our more recent work. Joint work with Swee Hong Chan and Greta Panova.
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