Triangle Lectures in Combinatorics

These are a series of combinatorial workshops, held once per semester, each on a Saturday. The series began with its first meeting in spring 2010. They rotate among the universities in and around the Research Triangle. Participants come from numerous colleges and universities within a few hours drive, and some from even farther away. These workshops are funded by the National Science Foundation, in particular enabling us to bring in four exciting speakers to give one hour talks each time as well as funding travel expenses for participants.

TLC steering committee: Patricia Hersh (U. Oregon), Ricky Liu (NCSU), Ezra Miller (Duke), Gabor Pataki (UNC Chapel Hill), and Cynthia Vinzant (NCSU).

TLC Fall 2020

Twentieth meeting: Saturday, November 14, 2020

Location: Zoom, hosted by UNC Greensboro

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

Tentative 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
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)

The links to access the talks and social events will be emailed to people who have registered for the conference, so make sure to register beforehand!

To register, please fill out this form.

List of pre-registered participants

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

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.

Past meetings:

Twentieth meeting: Saturday, November 14, 2020 at UNC Greensboro (online)
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)
Organizing Committee: Clifford Smyth (UNC Greensboro), Thomas McConville (Kennesaw State U.), Cynthia Vinzant (NCSU)
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Nineteenth meeting: Saturday, February 29, 2020 at UNC Charlotte
Speakers: Margaret Bayer (U Kansas), Michel Goemans (MIT), Svetlana Poznanović (Clemson), Cynthia Vinzant (NCSU)
Organizing Committee: Gabor Hetyei (UNC Charlotte), Ricky Liu (NCSU), Gabor Pataki (UNC Chapel Hill)
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Eighteenth meeting: Saturday, November 16, 2019 at NCSU
Speakers: Georgia Benkart (University of Wisconsin at Madison), Javier Peña (Carnegie Mellon University), Margaret Readdy (University of Kentucky), Alexander Yong (University of Illinois at Urbana-Champaign)
Organizing Committee: Patricia Hersh (NCSU), Gabor Hetyei (UNC-Charlotte), Kailash Misra (NCSU), Gabor Pataki (UNC Chapel Hill)
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Seventeenth meeting: Saturday, March 30, 2019 at Wake Forest University
Speakers:  James Haglund (University of Pennsylvania), Adam Marcus (Princeton University), Jennifer Morse (University of Virginia), Nathan Reading (North Carolina State University)
Organizing committee: Sarah Mason (Wake Forest), Ed Allen (Wake Forest), Patricia Hersh (NCSU), Cliff Smyth (UNC Greensboro)
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Sixteenth meeting: November 10, 2018 at UNC Chapel Hill
Speakers: László Babai (University of Chicago), Daniel Bienstock (Columbia), Rebecca Goldin (George Mason University), and Lek-Heng Lim (University of Chicago).
Organizing Committee: Prakash Belkale (UNC Chapel Hill), Gabor Pataki (UNC Chapel Hill), Richard Rimanyi (UNC Chapel Hill), and Seth Sullivant (NCSU).
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Fifteenth meeting: March 26, 2018 at NCSU
Speakers: Richard Kenyon (Brown), Karola Mészáros (Cornell), Gabor Hetyei (UNC-Charlotte), and Seth Sullivant (NCSU).
Organizing Committee: Patricia Hersh (NCSU), Ricky Liu (NCSU), and Cynthia Vinzant (NCSU)
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Fourteenth meeting: November 19, 2016 at NCSU
Speakers: Bruno Benedetti (U. Miami), Maria Chudnovsky (Princeton), Jeffery Lagarias (U. Michigan), Josephine Yu (Georgia Tech).
Organizing Committee: Ricky Liu (NCSU), Seth Sullivant (NCSU), and Cynthia Vinzant (NCSU)
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Thirteenth meeting: Saturday February 27, 2016 at UNC Greensboro
Speakers: Penny Haxell (U. Waterloo), Jeff Kahn (Rutgers), Greta Panova (U. Penn), Peter Winkler (Dartmouth).
Organizing Committee: Clifford Smyth, chair (UNC Greensboro), David Galvin (Notre Dame), and Patricia Hersh (NCSU).
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Twelfth meeting: Saturday October 3, 2015 at Duke
Speakers: Yuliy Baryshnikov (UIUC), Susan Holmes (Stanford), Dana Randall (Georgia Tech), and John Shareshian (Washington University in St. Louis).
Organizing Committee: Sayan Mukherjee, chair (Duke), John Harer (Duke), Patricia Hersh (NCSU), and Mauro Maggioni (Duke)
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Eleventh meeting: February 21, 2015 at NCSU
Speakers: Matthew Baker (Georgia Tech), Henry Cohn (Microsoft New England), Lionel Levine (Cornell), and Anne Schilling (UC Davis).
Organizing Committee: Ricky Liu (NCSU), Seth Sullivant (NCSU), and Cynthia Vinzant (NCSU)
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Tenth meeting: October 4, 2014, at High Point University
Speakers: Richard Ehrenborg (Kentucky), Robert Ghrist (Penn), Luis Serrano (U Quebec a Montreal), and Rekha Thomas (U. Washington).
Organizing Committee: Lindsay Piechnik (chair, High Point), Ed Allen (Wake Forest), Sarah Mason (Wake Forest), Seth Sullivant (NCSU), and Laurie Zack (High Point)
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Ninth meeting: February 22, 2014 at UNC-Chapel Hill.
Speakers: Shankar Bhamidi (UNC-Chapel Hill), Anders Buch (Rutgers), Pablo Parrilo (MIT), Eva Tardos (Cornell)
Organizing committee: Gabor Pataki (UNC-Chapel Hill), Lindsay Piechnik (High Point University), Scott Provan (UNC-Chapel Hill), Richard Rimanyi (UNC-Chapel Hill), Jack Snoeyink (UNC-Chapel Hill)
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Eighth meeting: September 21, 2013 at NCSU.
Speakers: George Andrews (Penn State), Matt Beck (San Francisco State University), Robin Pemantle (University of Pennsylvania), and Victoria Powers (Emory University)
Organizing committee: Michael Singer (NCSU), Carla Savage (NCSU), and Seth Sullivant (NCSU)
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Seventh meeting: February 9, 2013 at Wake Forest University.
Speakers: Louis Billera (Cornell), Rod Canfield (University of Georgia), Matthew Kahle (Ohio State University), Michelle Wachs (University of Miami)
Organizing committee: Sarah Mason (chair, Wake Forest University), Ed Allen (Wake Forest University), Alex Fink, (NCSU), Patricia Hersh (NCSU)
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Sixth meeting: September 22, 2012 at NCSU.
Speakers: Allen Knutson (Cornell), Vin de Silva (Pomona College), Richard Stanley (MIT), Lauren Williams (UC Berkeley).
Organizing committee: Alex Fink (NCSU), Patricia Hersh (NCSU), Carla Savage (NCSU).
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Fifth meeting: February 11, 2012 at Duke University.
Speakers: Alex Fink (NCSU), Sergey Fomin (Michigan), Nets Katz (Indiana University), Isabella Novik (University of Washington).
Organizing Committee: Christine Berkesch (Duke), Sonja Mapes (Duke), Ezra Miller (Duke).
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Fourth meeting: November 5, 2011 at UNC Chapel Hill.
Speakers: Thomas Lam (Michigan), Jesus De Loera (UC Davis), Ezra Miller (Duke), Doron Zeilberger (Rutgers)
Organizing committee: Prakash Belkale (UNC Chapel Hill), Gabor Pataki (UNC Chapel Hill), Robert Proctor (UNC Chapel Hill), Scott Provan (UNC Chapel Hill), Richard Rimanyi(UNC Chapel Hill).
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Third meeting: April 9, 2011 at NCSU.
Speakers: Prakash Belkale (UNC Chapel Hill), Vic Reiner (University of Minnesota), John Stembridge (University of Michigan), Stephanie van Willigenburg (UBC).
Organizing committee: Hoda Bidkhori (NCSU), Alex Fink (NCSU), Patricia Hersh (NCSU), Carla Savage (NCSU).
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Second meeting: September 25, 2010 at Duke.
Speakers: Alexander Barvinok (University of Michigan), Anne Shiu (Duke), Sami Assaf (MIT), Persi Diaconis (Stanford).
Organizing committee: Patricia Hersh (NCSU), Sonja Mapes (Duke), Ezra Miller (Duke).
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First meeting: February 6, 2010 at NCSU.
Speakers: Carla Savage (NCSU), Bernd Sturmfels (UC Berkeley), Ed Swartz (Cornell), Laszlo Szekely (University of South Carolina).
Organizing committee: Patricia Hersh (NCSU), Ezra Miller (Duke), Scott Provan (UNC), Nathan Reading (NCSU).
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