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 Fall 2023

Twenty-third meeting: Saturday, November 18, 2023

Location: SAS 1102, North Carolina State University, Raleigh

Parking: Local parking on SAS is free during the event

David Galvin (University of Notre Dame), Pamela E. Harris (University of Wisconsin at Milwaukee), Jianping Pan (NCSU), and Fan Wei (Duke University)

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

09:00 – 10:00am, welcome
10:00 – 11:00am, David Galvin
11:00 – 11:30am, coffee break
11:30 – 12:30pm, Fan Wei
12:30 – 2:30pm, lunch break
02:30 – 3:30pm, Jianping Pan
03:30 – 4:00pm, coffee break
04:00 – 5:00pm, Pamela E. Harris

To register, please fill out this form. This form includes a section with questions regarding funding.

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) and Clifford Smyth (UNC Greensboro)

Titles and Abstracts

David Galvin: Counting independent sets and colorings

In the late 1980’s, motivated by a problem from combinatorial group theory, Andrew Granville asked “at most how many independent sets can a regular graph admit?” This has proven to be a remarkably fruitful question, and one amenable to a remarkable variety of techniques, including graph containers, entropy and linear programming.
Although Granville’s initial question has by now been completely resolved (first by Kahn, for regular bipartite graphs, then by Zhao for all regular graphs), many related open questions remain.
I’ll discuss this problem, and some of its relatives, including maximizing the count of H-colorings of a regular graph, minimizing the count of H-colorings of a tree, and maximizing the count of independent sets in a regular graph in the presence of a bound on the largest independent set in the graph.

Pamela E. Harris: Finding needles in haystacks: Boolean intervals in the weak order of $\mathfrak{S}_n$

Finding and enumerating Boolean intervals in $W(\mathfrak{S}_n)$, the weak order of symmetric group $\mathfrak{S}_n$, can feel like trying to find needles in a haystack. However, through surprising connection to the outcome map of parking functions we provide a complete characterization and enumeration for Boolean intervals in $W(\mathfrak{S}_n)$. We show that for any $\pi\in\mathfrak{S}_n$, the number of Boolean intervals in $W(\mathfrak{S}_n)$ with minimal element $\pi$, is a product of Fibonacci numbers. This is joint work with Jennifer Elder, Jan Kretschmann, and J. Carlos Martínez Mori.

Jianping Pan: The Many Facets of Permutations

Permutations are fundamental objects in mathematics, biology and many other fields. Different presentations reveal different aspects of permutations, for instance, the one-line notation describes how a permutation’s pattern goes up and down while the reduced words highlight their construction through adjacent transpositions. In this talk, I will talk about certain tableaux, posets, and polytopes from permutations and the interplay between them. This talk is based on joint works with Banaian, Chepuri, Gunawan$^3$, Russel$^2$ and Tenner$^2$.

Fan Wei: Graph homomorphism density inequalities

Graph limits is a recently developed powerful theory in studying graphs from a continuous perspective. In this talk, we will show it is undecidable to prove general inequalities of homomorphism densities into (edge weighted) graphs. Then I will show how the perspective of graph limits helps with graph homomorphism inequalities and how to make advances in a common theme in extremal combinatorics: when does randomness give nearly optimal bounds?

Past meetings:

Twenty second meeting: Saturday, April 8, 2023 at NCSU
Speakers: Ed Allen (Wake Forest University, US), Nantel Bergeron (York University, Canada), Carly Klivans (Brown University, US), and Bruce Sagan (Michigan State University, US)
Organizing Committee: Laura Colmenarejo (NCSU), Sarah K. Mason (Wake Forest University), Nick Mayers (NCSU), Clifford Smyth (UNC Greensboro)
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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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