Speaker:  Igor Pak  (University of California, Los Angeles)

Title:  Correlations inequalities for posets

Abstract:

In Combinatorics, correlation inequalities often describe delicate inner properties of combinatorial structures; they are very intuitive but can be difficult to establish. For example, given that some edge e is in a random spanning tree T of a graph G, does it make it less likely that another edge e' is in T? Given that a random subgraph of G is Hamiltonian, does it make it less likely that it is also planar? The answer is yes in both cases, but for very different reasons.

In this talk I will concentrate on correlation inequalities for linear extensions of finite posets. I will start by reviewing the background: Stanley's log-concavity, Shepp's XYZ inequality, Bjorner-Wachs and Lam-Pylyavskyy inequalities for the number of standard Young tableaux. I will then discuss new correlation inequalities which we recently established with Swee Hong Chan. The talk is aimed at a general audience.