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: Laura Colmenarejo (NC State), Sean English (UNC Wilmington), Gabor Pataki (UNC Chapel Hill), Clifford Smyth (UNC Greensboro), and Fan Wei (Duke University)
Former TLC steering committee: Nathan Reading (NC State), Ricky Liu (NC State), Ezra Miller (Duke University), and Gabor Pataki (UNC Chapel Hill).
TLC Spring 2025
Twenty-sixth meeting: Saturday, April 19, 2025
Location: SAS 1102 at NC State
Parking: Free parking at the university during the weekend, starting on Friday at 5 pm. Google Maps directions for parking at SAS Hall.
Speakers:
Marcelo Aguiar (Cornell University)
Kyle Celano (Wake Forest University)
Ruth Luo (University of South Carolina)
Rosa Orellana (Dartmouth College)
Tentative Conference Schedule (all times in EST)
(Abstracts will be posted below)
09:00 – 10:00am, welcome
10:00 – 11:00am, Rosa Orellana
11:00 – 11:30am, coffee break
11:30 – 12:30pm, Ruth Luo
12:30 – 2:30pm, lunch break
02:30 – 3:30pm, Marcelo Aguiar
03:30 – 4:00pm, coffee break
04:00 – 5:00pm, Kyle Celano
Registration and Funding: Please, complete the following GoogleForm, which contains questions regarding funding too
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)
Funding provided by NSF
Titles and Abstracts
Marcelo Aguiar: Descents for cones of a real hyperplane arrangement
Reading a permutation from left to right and recording the positions where the values decrease yields the descent set of the permutation. More generally, descents may be attached to elements of a finite Coxeter group. In this talk we will discuss a different extension of the notion of descents, to the setting of real hyperplane arrangements. The notion on which this is based is the Tits product, an operation that exists on the set of faces of such an arrangement. The talk will center around this fundamental notion and include a discussion of faces, cones, and descents, together with lots of illustrations. No previous familiarity with hyperplane arrangements will be assumed.
Kyle Celano: A new proof that K^{-1}K=I
Of course, a matrix times its inverse is the identity. However, when the matrix and its inverse have combinatorial interpretations, one can ask for a combinatorial proof. The Kostka matrix K is the transition matrix between two symmetric function bases, and has a combinatorial interpretation in terms of semistandard Young tableaux. Eğecioğlu and Remmel produced a combinatorial proof of KK^{-1} = I, but were unable to find a proof for K^{-1}K=I. Partial progress on this was made by Sagan and Lee and the full proof by Loehr and Mendes of the identity requires the use of the bijective matrix algebra and the Eğecioğlu and Remmel map. In this talk, we present a full combinatorial proof of K^{-1}K=I independent of the Eğecioğlu and Remmel map utilizing a new combinatorial interpretation of K^{-1} found by Allen and Mason. This requires us to leave the land of symmetric functions and journey into noncommutative symmetric function territory before eventually returning home. Joint work with E. E. Allen and S. K. Mason.
Ruth Luo: Extremal problems for cycles in graphs and hypergraphs
Extremal combinatorics studies the maximum size a combinatorial object can have while forbidding a given substructure. Equivalently, it studies the minimum size of an object that forces the existence of the substructure. One of the most well studied areas in this field is that of Hamiltonian cycles in graphs. In the first half of this talk, we give a brief historical overview of extremal problems for cycles in graph theory. In the second half, we introduce analogues of cycles in hypergraphs called Berge cycles. We then discuss some recent developments in extremal hypergraph theory and how these relate to or differ from classical results for graphs.
Rosa Orellana: Reconstructing trees from their chromatic symmetric function
In 1995, Stanley introduced the chromatic symmetric function (CSF) as a generalization of the chromatic polynomial, which counts the number of proper colorings of a graph. A central question is determining what structural properties of a graph can be recovered from its CSF. Properties such as connectivity, the number of connected components, the presence of cycles, and the number of triangles are easily identifiable. However, while the CSF encodes many structural properties, it does not fully determine a graph, as non-isomorphic graphs with the same CSF exist—though all known examples contain cycles. The tree isomorphism conjecture posits that no two non-isomorphic trees share the same CSF. In this talk, I will discuss progress toward resolving this conjecture using the star basis of symmetric functions.
Past meetings:
Twenty-fifth meeting: Saturday, September 21, 2024 at UNC Wilmington
Speakers: Sarah Mason (Wake Forest University, US), Nick Mayers (NC State University, US), Corrine Yap (Georgia Tech, US), and Shira Zerbib (Iowa State University, US)
Organizing Committee: Laura Colmenarejo (NC State), Sean English (UNC Wilmington, US), and Clifford Smyth (UNC Greensboro)
Local Organizing Committee: Lilit Martirosyan (UNC Wilmington, US), and Erik Slivken (UNC Wilmington, US)
More information
Twenty-fourth meeting: Saturday, March 23, 2024 at UNC Greensboro
Speakers: Sean English (UNC Wilmington, US), Emily Heath (Iowa State University, US), Jacob Matherne (North Carolina State University, US), and Cosmin Pohoata (Emory University, US)
Organizing Committee: Laura Colmenarejo (NCSU), Sean English (UNC Wilmington, US), and Clifford Smyth (UNC Greensboro)
More information
Twenty third meeting: Saturday, November 18, 2023 at NCSU
Speakers: David Galvin (University of Notre Dame, US), Pamela E. Harris (University of Wisconsin at Milwaukee, US), Jianping Pan (North Carolina State University, US), and Fan Wei (Duke University, US)
Organizing Committee: Laura Colmenarejo (NCSU), Clifford Smyth (UNC Greensboro)
More information
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)
More information
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)
More information
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)
More information
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)
More information
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)
More information
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)
More information
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).
More information
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)
More information
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)
More information
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).
More information
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)
More information
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)
More information
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)
More information
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)
More information
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)
More information
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)
More information
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).
More information
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).
More information
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).
More information
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).
More information
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).
More information
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).
More information