# 60th William J. Spencer Lecture

Sara Billey, University of Washington, Seattle, will present the 60^{th} William J. Spencer Lecture titled “Some Theorems in Asymptotic Algebraic Combinatorics" as part of the Mathematics Department Women Lecture Series in celebration of the 50^{th} anniversary of the Association for Women in Mathematics.

The abstract for the lecture is: Asymptotic Combinatorics is a branch of Mathematics that looks at limiting distributions of combinatorial formulas. Our recent work has focused on generalizations of a classic formula for standard Young tableaux called the Hook Length Formula and its generalizations to using the major index statistic. Further examples include Stanley’s q-hook-content formula for semistandard tableaux and q-hook length formulas of Björner–Wachs related to linear extensions of labeled forests. We show that, while these limiting distributions are “generically” asymptotically normal, there are uncountably many non-normal limit laws. More precisely, we introduce and completely describe the compact closure of the moduli space of distributions of these statistics in several regimes. The additional limit distributions involve generalized uniform sum distributions which are topologically parameterized by certain decreasing sequence spaces with bounded 2-norm. The closure of the moduli space of these distributions in the Lévy metric gives rise to the moduli space of DUSTPAN distributions. As an application, we completely classify the limiting distributions of the size statistic on plane partitions fitting in a box. This talk is based on joint work with Joshua Swanson at USC

(https://arxiv.org/abs/2010.12701).

The Math Department is a part of K-State’s College of Arts and Sciences. To learn more about opportunities in Math at K-State, visit the math department website.

Streamed live: https://youtu.be/kOgzewZY8_M

Thursday, October 28 at 2:30pm to 3:20pm

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