Igor Pak: Asymptotics of the number of standard Young tableaux of skew shape

Abstract

Consider random standard Young tableaux of a fixed skew shape. What do they look like as the shapes get large? To be precise, in this talk, we analyze the asymptotics of the number of standard Young tableaux of large skew shapes, which allow to give partial answers to this questions in a variety of special cases. We present new bounds and discuss how they compare with the existing general bounds on the numbers of linear extensions of the corresponding posets. Our approach is based on Naruse's hook-length formula which I will also explain, and new estimates on LR-coefficients. The talk is aimed at a general audience and assumes no previous knowledge of the subject. Based in part on joint work with Alejandro Morales and Greta Panova.