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: Nathan Reading (NCSU), Ricky Liu (NCSU), Ezra Miller (Duke University), and Gabor Pataki (UNC Chapel Hill).

TLC Spring 2023

Twenty-second meeting: Saturday, April 8, 2023

Location: SAS 1102, North Carolina State University, Raleigh

Parking: Local parking on SAS is free during the event

Ed Allen (Wake Forest University, US), Nantel Bergeron (York University, Canada), Carly Klivans (Brown University, US), and Bruce Sagan (Michigan State University, US).

Tentative Conference Schedule (all times in EST)
(Abstracts can be found below)

09:00 – 10:00am, welcome
10:00 – 11:00am, Nantel Bergeron
11:00 – 11:30am, coffee break
11:30 – 12:30pm, Caroline Klivans
12:30 – 2:30pm, lunch break
02:30 – 3:30pm, Edward Allen
03:30 – 4:00pm, coffee break
04:00 – 5:00pm, Bruce Sagan

To register, please fill out this form.

Lunch break: 
There are many restaurants and take-out places around campus. In particular, in Hillsborough street you can find Bul-box, Lemon & lime, Guasaca, Chipotle, Jasmin & Olive, Player’s retreat, David’s dumplings, among others. Also in the Cameron Village, which is ~15 minutes walking-distance, you can find other places like CAVA, Cantina 18, Kale me crazy, and many more.

Organizing Committee: Laura Colmenarejo (NCSU), Sarah K. Mason (Wake Forest University), Nick Mayers (NCSU), and Clifford Smyth (UNC Greensboro)

Titles and Abstracts

Ed Allen: Tunnel hook fillings and a combinatorial interpretation of the noncommutative inverse Kostka matrix

The inverse Kostka matrix is the transition matrix between the Schur functions and the complete homogeneous symmetric functions. Eğecioğlu and Remmel developed a combinatorial interpretation for the entries of this matrix using special rim hooks to decompose Ferrers partition diagrams. Recently, Berg, Bergeron, Saliola, Serrano, and Zabrocki introduced the immaculate basis in the space of noncommutative symmetric functions (NSYM) which are an analogue of Schur functions. We generalize Eğecioğlu’s and Remmel’s special rim hooks by introducing new diagrams for skews of integer sequences (involving colored cells) and filling the diagrams with objects we call tunnel hook fillings. This method also gives a combinatorial interpretation to the expansion of monomial quasisymmetric functions into dual immaculates. Finally, we show how tunnel hook fillings can be used to extend Campbell’s results on ribbon decompositions of immaculate functions to a larger class of shapes.

Nantel Bergeron: The excedance quotient of the Bruhat order, Quasisymmetric Varieties and Temperley-Lieb algebras

Let be the ring of polynomial in n variables over the rationals and consider the ideal generated by quasisymmetric polynomials without constant term. It was shown by J. C. Aval, F. Bergeron and N. Bergeron that , the n-th Catalan number. In the present work, we explain this phenomenon by defining a set of permutations with the following properties: first, is a basis of the Temperley–Lieb algebra , and second, when considering as a collection of points in , the top-degree homogeneous component of the vanishing ideal is . Our construction has a few byproducts which are independently noteworthy. We define an equivalence relation on the symmetric group using weak excedances and show that its equivalence classes are naturally indexed by noncrossing partitions. Each equivalence class is an interval in the Bruhat order between an element of and a 321-avoiding permutation. Furthermore, the Bruhat order induces a well-defined order on . Finally, we show that any section of the quotient gives an (often novel) basis for .
This is joint work with L. Gagnon.

Carly Klivans: The Mathematics of Chip-Firing

Chip-firing processes are discrete dynamical systems. A commodity (chips, sand, dollars) is exchanged between sites of a network according to simple local rules. Although governed by local rules, the long-term global behavior of the system reveals unexpected properties, including intricate fractal-like patterns. Early results related chip-firing to classic combinatorial objects such as spanning trees, parking functions, and matroids. In recent years, chip-firing has seen much activity in new directions. Connections have been made, for example, between chip-firing and Coxeter groups, binomial ideals, and Riemann surfaces. In this talk, I will give a broad survey of the theory of chip-firing and its many ties to algebraic combinatorics.

Bruce Sagan: Stirling numbers for complex reflection groups

The ordinary Stirling numbers count set partitions and permutations of
{1, 2, . . . , n} by number of subsets and number of cycles, respectively. We show how to generalize these concepts to a complex reflection group. The ordinary Stirling numbers are recovered in type A. It turns out that often these Stirling numbers can be expressed in terms of elementary and homogeneous symmetric functions. We also make a connection with super coinvariant algebras. All terminology concerning Stirling numbers, symmetric functions, and complex reflection groups will be defined. This is joint work with Joshua Swanson.

Past meetings:

Twenty first meeting: Saturday, December 3, 2022 at UNC Greensboro (in person)
Speakers: Jeremy L. Martin (University of Kansas), Erik Slivken (University of North Carolina Wilmington), Catherine Yan (Texas A&M University), and Yan Zhuang (Davidson College)
Organizing Committee: Laura Colmenarejo (NCSU), Sarah K. Mason (Wake Forest University), Clifford Smyth (UNC Greensboro)
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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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