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 Fall 2025
Twenty-seventh meeting: Saturday, November 1, 2025
Location: Gross Hall Room 107, Duke University
Parking: General parking information can be found here. In particular, the Bryan Center lot is $2 per hour and it is located 5 minutes walking distance to Gross Hall. We have a limited amount of parking passes available to those carpooling or coming from further away. Please, contact Fan Wei (Duke University) for more details about it. Note that these are first come, first served, and so we may run out of them.
For Duke people who do not have a parking pass, we recommend purchasing an After-Hours Permit, which allows parking in almost all campus lots (including the Chemistry Lot) during weekends. The permit itself is free, with only a $5 administrative fee and a $0.15 credit card processing fee. More details are available here.
Please, see this map for more details on the different parking lots and the appropriate entrances depending on the construction.
Speakers:
Jacob Fox (Stanford University)
Igor Pak (UCLA)
Shubhangi Saraf (University of Toronto)
Richard Stanley (MIT, emeritus)
Tentative Conference Schedule (all times in EST)
(Abstracts will be posted below)
09:00 – 10:00am, welcome
10:00 – 11:00am, Richard Stanley
11:00 – 11:30am, coffee break & poster session
11:30 – 12:30pm, Jacob Fox
12:30 – 2:30pm, lunch break
02:30 – 3:30pm, Shubhangi Saraf
03:30 – 4:00pm, coffee break & poster session
04:00 – 5:00pm, Igor Pak
5:00 – 5:30pm poster session
Registration and Funding: Please, fill out this form to register for the conference and to request funding. Registration is free and funding is provided by NSF. If you have any questions, feel free to email any of the organizers.
We are asking that participants pre-register if possible, as it is very helpful for planning our coffee breaks and obtaining funding to support these events.
Poster session [application closed]: Please, fill out this form if you are interested in presenting a poster during the conference. The form contains a lot of details and relevant information, so please read it carefully.
Note that only junior researchers (students, postdocs, and tenure-track faculty) will present during the conference. Senior faculty should encourage their students and more junior colleagues to apply. For students, the poster they present must be on joint research with their advisor or a more senior researcher, and their name must appear as one of the authors.
Lunch break: The best option walking distance is the student center cafeteria. Menu and opening hours can be found here.
Organizing Committee: Benjamin Rossman (Duke University), Clifford Smyth (UNC Greensboro), and Fan Wei (Duke University)
Funding provided by NSF
Titles and Abstracts
Jacob Fox: Additive combinatorics without addition and applications
We show through purely combinatorial means that group structure is superfluous in some fundamental problems in additive combinatorics. This leads to the solution of longstanding open problems in Ramsey theory, additive combinatorics, random graphs, and the mathematical theory of communication. Based on joint work with David Conlon, Huy Tuan Pham, and Liana Yepremyan.
Igor Pak: Inverse counting problems
In Combinatorics, a typical question asks to count the number of combinatorial objects of a certain kind, e.g. the number of spanning trees or perfect matchings in a given graph. In the past few years, the inverse questions have also become popular, e.g. what is the smallest size graph which has a given number of spanning trees, or of a given number of perfect matchings? These questions turned out to be deeply related to computational complexity and to several classic problems in extremal combinatorics and number theory. In the first part of the talk I will give a broad overview of several combinatorial functions where this inverse problem has been resolved. I will then discuss our recent work on two inverse problems above via Zaremba type results on continued fractions.
Shubhangi Saraf: The complexity of factors of polynomials
I will talk about a recent result showing that algebraic formulas and constant-depth circuits are closed under taking factors. In other words, the complexity of factors of polynomials computable by algebraic formulas or constant depth algebraic circuits is not much more than the complexity of the original polynomial itself. This result turns out to be an elementary consequence of a fundamental and surprising result of Furstenberg from the 1960s, which gives a non-iterative description of the power series roots of a bivariate polynomial. Combined with standard structural ideas in algebraic complexity, we observe that this theorem yields the desired closure results. We will see applications of this result to deterministic algorithms for factoring, hardness/randomness tradeoffs, as well as GCD computation of polynomials. This talk is based on joint works with Somnath Bhattacharjee, Mrinal Kumar, Shanthanu Rai, Varun Ramanathan and Ramprasad Saptharishi.
Richard Stanley: Alternating Permutations and Sprout Symmetric Functions
An alternating permutation of 1,2,..,n is a permutation a_1, a_2, …, a_n of 1,2,…,n satisfying a_1 > a_2 < a_3 > a_4 < … a_n. Motivated by a result of Amdeberhan-Ono-Singh on a certain theta function of Ramanujan, we define certain symmetric functions A_n related to alternating permutations. The A_n’s belong to a special class of symmetric functions that we call sprout symmetric functions.
The theory of sprout symmetric functions assumes a knowledge of the theory of symmetric functions. Since we are not assuming such knowledge from listeners, we will give a long review of some interesting aspects of alternating permutations and only a taste of the theory of sprout symmetric functions. Most notably, the question of when sprout symmetric functions are Schur positive is closely related to the Edrei-Thoma theorem from the theory of total positivity.
Past meetings:
Twenty-sixth meeting: Saturday, April 19, 2025 at NC State
Speakers: Marcelo Aguiar (Cornell University, US), Kyle Celano (Wake Forest University, US), Ruth Luo (University of South Carolina, US), and Rosa Orellana (Dartmouth College, US)
Organizing Committee: Laura Colmenarejo (NC State), and Clifford Smyth (UNC Greensboro)
More information
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