Triangle Lectures in Combinatorics (TLC)

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).

Upcoming meeting: Saturday, March 24, 2018, 9am-5pm
Location: North Carolina State University, Raleigh
Lecture Hall: SAS Room 1102

Speakers: Richard Kenyon (Brown), Karola Mészáros (Cornell), Ileana Streinu (Smith), and Seth Sullivant (NCSU)

Preregistration: please send email to (Patricia Hersh) to preregister. This is very helpful in our planning how much coffee, etc. to have at coffee breaks and for our obtaining funding to support these meetings.

Participant Travel Expense Reimbursement: 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. To apply for funding please fill out the form here.

Conference schedule:
9:15-10am, coffee and small breakfast
10-11am, Richard Kenyon (Brown),  Harmonic functions and the chromatic polynomial
11-11:30am, coffee break
11:30am-12:30pm, Karola Mészáros (Cornell),  Flow polytopes in combinatorics and algebra
12:30-2:30pm, lunch break
2:30-3:30pm, Ileana Streinu (Smith),  Characterizing 3D rigidity: combinatorial and geometric obstructions
3:30-4pm, coffee break
4-5pm, Seth Sullivant (NCSU),  Maximum agreement subtrees
6pm, informal conference dinner

Practical details:

Parking: You may park right outside SAS Hall for free. Here is a map of the campus. On Saturdays, you can park anywhere on campus that is not specifically marked as being restricted (e.g. handicap spots are still off limits). We are hopeful that you won't need any lot except the one by SAS Hall. SAS Hall is at the upper right of the map, and the parking lot is near the intersection of Stinson Drive and Boney Dr. A good back-up option for parking is the Coliseum Parking Deck.

The room: SAS Hall 1102 is the room immediately to your right when you enter from the parking lot. If you enter from the courtyard side, go down the long stairway or the elevators.

Hotel recommendations: We have a block of rooms reserved at the Doubletree by Hilton Raleigh - Brownstone (919-828-0811) accessed by this link. Also within a short walk of the math department is Aloft Raleigh (919-828-9900). About 1.5 miles away in downtown Raleigh (also walkable, but somewhat long walk) is the Holiday Inn Raleigh Downtown (919-832-0501). Those with cars might also consider hotels farther away such as Holiday Inn Express (919-854-0001) 3741 Thistledown Drive (near Centennial Campus) as well as various hotel choices on Wake Town Drive, which is near numerous good restaurants; some such hotels (all right next to each other on Wake Towne Drive) are Marriott Courtyard (919-821-3400), Hampton Inn (919-828-1813), or Extended Stay America (919-829-7271).

Airport: Raleigh-Durham International Airport is 20-30 minutes drive from NCSU. Taxi fare is about $30.

Registered Participants (so far):

Aaron Abrams (Washington and Lee U.)
Daniel Bernstein (NCSU)
Cashous Bortner (NCSU)
Michael Bremen-McKay (NCSU)
Dylan Bruce (NCSU)
Jessie Copher (NCSU)
Darij Grinberg (U. Minnesota)
Patricia Hersh (NCSU)
Gabor Hetyei (UNC Charlotte)
Ben Hollering (NCSU)
Rick Kenyon (Brown)
Stephen Lacina (NCSU)
Lionel Levine (Cornell)
Ricky Liu (NCSU)
Molly Lynch (NCSU)
Aida Maraj (U. Kentucky)
Sarah Mason (Wake Forest)
Emily Meehan (Gallaudet U.)
Karola Meszaros (Cornell)
Kailash Misra (NCSU)
Walter Morris (George Mason University)
Wesley Nelson (NCSU)
Gabor Pataki (UNC Chapel Hill)
Rodney Reid
Radmila Sazdanovic (NCSU)
Jack Snoeyink (UNC Chapel Hill)
Avery St. Dizier (Cornell)
Grace Stadnyk (NCSU)
Michael Strayer (UNC Chapel Hill)
Ileana Streinu (Smith College)
Seth Sullivant (NCSU)
Julianne Vega (U. Kentucky)
Shira Viel (NCSU)
Andrés R. Vindas Meléndez (U. Kentucky)
Cynthia Vinzant (NCSU)
Michael Weselcouch (NCSU)
Anita Yadavalli (NCSU)
Sercan Yildiz (UNC Chapel Hill and SAMSI)

Local organizing committee: Patricia Hersh (NCSU), Ricky Liu (NCSU), and Cynthia Vinzant (NCSU)

Talk titles and abstracts:

Richard Kenyon (Brown)

Title: Harmonic functions and the chromatic polynomial

Abstract: The chromatic polynomial X(n) of a graph counts the number of proper colorings with n colors. For each negative integer n we show how to compute |X(n)| as the degree of a certain rational mapping. This mapping arises from the "Dirichlet problem" of finding a harmonic function with fixed boundary values. Our techniques also allows us to equate |X(n)| with a certain set of acyclic orientations of a related graph. This is joint work with Wayne Lam.

Karola Mészáros (Cornell)

Title: Flow polytopes in combinatorics and algebra

Abstract: The flow polytope FG(v) is associated to a graph G on the vertex set {1,..., n} with edges directed from smaller to larger vertices and a netflow vector v=(v1,..., vn) in Zn. The points of FG(v) are nonnegative flows on the edges of G so that flow is conserved at each vertex. Postnikov and Stanley established a remarkable connection of flow polytopes and Kostant partition functions two decades ago, developed further by Baldoni and Vergne. Since then, flow polytopes have been discovered in the context of Schubert and Grothendieck polynomials and the space of diagonal harmonics, among others. This talk will survey a selection of results about the ubiquitous flow polytopes.

Ileana Streinu (Smith College)

Title: Characterizing 3D rigidity: combinatorial and geometric obstructions

Abstract: In spite of many conjectures and approaches spanning the last 30 years, a combinatorial characterization of 3D rigid graphs (generic bar-and-joint frameworks) remains elusive. I will discuss a few approaches, all of which fall short of solving the problem due to various combinatorial or geometric obstructions. They include "classical" results (the non-matroidal nature of the underlying "3n-6" sparsity counts and the failure of natural inductive constructions), as well as more recent ones: (1) the existence of arbitrarily large nucleation-free graphs (joint work with M. Sitharam and J. Cheng) and (2) a generalization from the finite to the periodic setting, in which a (rather unusual) definition of genericity has led to a combinatorial characterization via quotient graphs (joint work with C. Borcea) .

Seth Sullivant (NCSU)

Title: Maximum agreement subtrees

Abstract: Probability distributions on the set of trees are fundamental in evolutionary biology, as models for speciation processes. These probability models for random trees have interesting mathematical features and lead to difficult questions at the boundary of combinatorics and probability. This talk will be concerned with the question of how much two random trees have in common, where the measure of commonality is the size of the largest agreement subtree. The case of maximum agreement subtrees of pairs of random comb trees is equivalent to studying longest increasing subsequences of random permutations, and has connections to random matrices. This elementary talk will try to give a sense of what is known (not very much) and what is unknown (lots!) about this problem.

Past meetings:

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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