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 (NCSU), Ricky Liu (NCSU), Ezra Miller (Duke), Gabor Pataki (UNC Chapel Hill), and Cynthia Vinzant (NCSU).

TLC Spring 2020

Upcoming meeting: Saturday, February 29, 2020
Location: UNC Charlotte
Room: Fretwell 100

Speakers: Margaret Bayer (U Kansas), Michel Goemans (MIT), Svetlana Poznanović (Clemson), Bruce Sagan (Michigan State)

Organizing Committee: Gabor Hetyei (UNC Charlotte), Ricky Liu (NCSU), Gabor Pataki (UNC Chapel Hill)

Registration and funding applications:
To register and/or apply for funding, please fill out this form.

We are asking that participants preregister if possible, as preregistration is very helpful for planning our coffee breaks and obtaining funding to support these meetings. We have some funding available for some participants, especially for early-career participants. Most of this is restricted to US citizens and permanent residents, and what is available to others still requires that the participants be employed at a U.S. university. You will have the opportunity to apply for funding when registering for the conference.

Conference schedule

9:15-10am, coffee and light breakfast
10-11am, Margaret Bayer, Counting flags in Eulerian posets: The cd-index
11-11:30am, coffee break
11:30am-12:30pm, Michel Goemans, Semidefinite Programming Relaxation of MAXCUT: A Survey
12:30-2:30pm, lunch break
2:30-3:30pm, Svetlana Poznanović, Hecke insertion and maximal increasing and decreasing sequences in fillings of polyominoes
3:30-4pm, coffee break
4-5pm, Bruce Sagan, Stirling numbers for complex reflection groups
6pm, informal conference dinner

Hotel: We have a block of rooms at Drury Inn that is available until January 27.

Parking: There is free parking on campus near Fretwell in the East Deck and Lot 5. (Campus map)

List of preregistered participants

Airport: Charlotte Douglas International Airport is 20-30 minutes drive from UNC Charlotte. Taxi fare is about $30.

Talk titles and abstracts:

Margaret Bayer (U Kansas)

Title: Counting flags in Eulerian posets: The cd-index

The face lattices of convex polytopes and intervals in the Bruhat order of Coxeter groups are examples of Eulerian posets. The flag vector of an Eulerian poset counts the sequences of elements of specified ranks. The linear relations that hold for the flag vectors of all Eulerian posets are known, and it turns out the dimension of the flag vectors for posets of fixed rank is a number in the Fibonacci sequence. Jonathan Fine discovered that the flag vectors could be efficiently coded in a vector called the cd-index. This talk discusses the history of the cd-index, with a focus on inequalities, connections with other combinatorial parameters and relations to algebraic structures.

Michel Goemans (MIT)

Title: Semidefinite Programming Relaxation of MAXCUT: A Survey

I will discuss the semidefinite programming relaxation of the maximum cut problem in graphs and the random hyperplane rounding scheme, proposed together with David Williamson over 25 years ago. The talk will cover several extreme classes of instances involving geometry and spectral graph theory, their connections to inapproximability and social choice theory, and a novel, alternate rounding scheme.

Svetlana Poznanović (Clemson)

Title: Hecke insertion and maximal increasing and decreasing sequences in fillings of polyominoes

In this talk we will give a proof that the number of 01-fillings of a given stack polyomino (a polyomino with justified rows whose lengths form a unimodal sequence) with at most one 1 per column which do not contain a fixed-size northeast chain and a fixed-size southeast chain, depends only on the set of row lengths of the polyomino. The proof is via a bijection between fillings of stack polyominoes which differ only in the position of one row and uses Hecke insertion and jeu de taquin for increasing tableaux. We will also survey how this work relates to other results about chains in fillings of polyominoes as well as graphs and set partitions and discuss some possible and impossible extensions.

Bruce Sagan (Michigan State)

Title: Stirling numbers for complex reflection groups

Let G be a finite, irreducible complex reflection group. We propose defining Stirling numbers of the first and second kind for G as the Whitney numbers of the first and second kind for the intersection lattice L(G). The ordinary Stirling numbers are recovered in type A. We show that often these Stirling numbers can be expressed in terms of elementary and homogeneous symmetric functions. When G is a Coxeter group, we also investigate ordered Stirling analogues obtained by relating L(G) and G‘s Coxeter complex. Various statistics on L(G) yield q-analogues of unordered and ordered Stirling numbers of the second kind, one of which has appeared in a recent super covariant conjecture of Zabrocki. This is joint work with Robin Sulzgruber and Joshua Swanson.

Past meetings:

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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