# Fall 2020

**Twentieth meeting: Saturday, November 14, 2020
Location: Zoom, hosted by UNC Greensboro**

**Speakers:** Sara Billey (University of Washington, Seattle), Hao Huang (Emory University), Igor Pak (University of California, Los Angeles), and Nathan Williams (University of Texas, Dallas)

**Conference Schedule** (all times in EST)

12:20 – 12:30pm, welcome

12:30 – 1:10pm, Sara Billey, Limit Laws for *q*-Hook Formulas (slides, video)

1:10 – 1:30pm, break

1:30 – 2:10pm, Nathan Williams, Independence Posets (slides, video)

2:10 – 3:30pm, “coffee break” at gather.town

3:30 – 4:10pm, Hao Huang, Interlacing methods in Extremal Combinatorics (slides, video)

4:10 – 4:30pm, break

4:30 – 5:10pm, Igor Pak, Kronecker coefficients: bounds and complexity (slides, video)

**Organizing Committee:** Clifford Smyth (UNC Greensboro), Thomas McConville (Kennesaw State U.), Cynthia Vinzant (NCSU)

**Participant List (Total=84):**

Abeer Al Ahmadieh (University of Washington)

Edward Allen (Wake Forest University)

Yeva Ashari (Bandung Institute of Technology, Indonesia)

Matt Baker (Georgia Tech)

Margaret Bayer (University of Kansas)

Sara Billey (University of Washington)

Sarah Birdsong (University NC Charlotte)

Swee Hong Chan (UCLA)

Shih-Wei Chao (University of North Georgia)

Sunita Chepuri (University of Michigan)

Sebi Cioaba (University of Delaware)

Jane Coons (North Carolina State University)

Joseph Cummings (University of Kentucky)

Richard Ehrenborg (University of Kentucky)

Thomas Elgin (NC State)

Sergi Elizalde (Dartmouth)

Jennifer Galovich (St. John’s University)

Yibo Gao (MIT)

Ira Gessel (Brandeis University)

Andrey Glubokov (Ave Maria University)

Curtis Greene (Haverford College)

Adam Gregory (University of Florida)

Darij Grinberg (Drexel University)

Emily Gunawan (University of Oklahoma)

William Gustafson (University of Kentucky)

Derek Hanely (University of Kentucky)

Patricia Hersh (University of Oregon)

Gabor Hetyei (UNC Charlotte)

Benjamin Hollering (North Carolina State University)

Sam Hopkins (University of Minnesota)

Hao Huang (Emory University)

Sam Jeralds (University of North Carolina, Chapel Hill)

Joe Johnson (North Carolina State University)

Nidhi Kaihnsa (Brown University)

Elizabeth Kelley (University of Minnesota)

Kang-Ju Lee (Seoul National University)

Michael Levet (University of Colorado Boulder)

Hsin-Chieh Liao (University of Miami)

Patrick Liscio (Brown University)

Ricky Liu (North Carolina State University)

Xinyu Ma (UCLA)

Barbara Margolius (Cleveland State University)

Sarah Mason (Wake Forest University)

Thomas McConville (Kennesaw State)

Geoffrey McKenna (industry)

Emily Meehan (Gallaudet University)

Walter Morris (George Mason University)

Alperen Ozdemir (Georgia Tech)

Igor Pak (UCLA)

Joseph Pappe (UC Davis)

Brendan Pawlowski (University of Southern California)

Robert Proctor (UNC-CH Math)

Nicholas Proudfoot (University of Oregon)

Arvind Ramaswami (Georgia Institute of Technology)

Margaret Readdy (University of Kentucky)

Nathan Reading (North Carolina State University)

Richard Rimanyi (UNC Chapel Hill)

Heather Russell (University of Richmond)

Bruce Sagan (MSU)

Carla Savage (North Carolina State University)

Kalila Sawyer (Colorado School of Mines)

Anne Schilling (UC Davis)

Clifford Smyth (UNCG)

Richard Stanley (U. Miami & M.I.T.)

Michael Strayer (Hampden-Sydney College)

Sheila Sundaram (Pierrepont School)

Joshua Swanson (UCSD)

Arthur Tanjaya (Cornell University)

Ashley Tharp (NCSU)

Sean Thompson (North Carolina State University)

Mark Tiefenbruck (Institute for Defense Analyses)

Angela Vichitbandha (North Carolina State University)

Cynthia Vinzant (NCSU)

Matias von Bell (University of Kentucky)

Lily Wang (University of Michigan)

Shiyun Wang (USC)

Anna Weigandt (University of Michigan)

Nathan Williams (UT Dallas)

Peter Winkler (Dartmouth)

Rupei Xu (UT Dallas )

Alfi y. Zakiyyah (Bina Nusantara University)

Chi Ho Yuen (Brown University)

Chenchen Zhao (USC)

Yan Zhuang (Davidson College)

**Talk titles and abstracts:**

**Sara Billey** (UW)

Title: Limit Laws for *q*-Hook Formulas

Abstract: Various asymptotic aspects of the Hook Length Formula for
standard Young tableaux have been studied recently in combinatorics and probability. In this talk, we study the limiting distributions that come from random variables associated to 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 UCSD.

**Nathan Willams** (UT Dallas)

Title: Independence Posets

Abstract: Let G be an acyclic directed graph. For each vertex of G, we define an involution on the independent sets of G. We call these involutions flips, and use them to define the independence poset for G — a new partial order on independent sets of G. Our independence posets are a generalization of distributive lattices, eliminating the lattice requirement: an independence poset that is a graded lattice is always a distributive lattice. Many well-known posets turn out to be special cases of our construction.

**Hao Huang ** (Emory University)

Title: Interlacing methods in Extremal Combinatorics

Abstract: Extremal Combinatorics studies how large or how small a collection of finite objects could be, if it has to satisfy certain restrictions. In this talk, we will discuss how eigenvalue interlacings lead to various interesting results in Extremal Combinatorics, including the Erdos-Ko-Rado Theorem and its degree version, an isodiametric inequality for discrete cubes, and the resolution of a thirty-year-old open problem in Theoretical Computer Science, the Sensitivity Conjecture.

**Igor Pak** (UCLA)

Title: Kronecker coefficients: bounds and complexity

Abstract: Kronecker coefficients of the symmetric group remain deeply mysterious in part because they famously lack a combinatorial interpretation. In fact, so little is known about them, even the weakest lower bounds can become groundbreaking. I will give a broad survey of recent results on the subject, concentrating on the upper bounds and the computational complexity aspects. I will also discuss various open problems on Kronecker coefficients, and relate them to known results and open problems on Littlewood-Richardson coefficients.