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 and the National Security Agency, 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), Ezra Miller (Duke), Gabor Pataki (UNC Chapel Hill), Nathan Reading(NCSU), Seth Sullivant (NCSU), and Cynthia Vinzant (NCSU).

Upcoming meeting: Saturday February 27, 2016, 9:15am -- 6pm.

Location: Sullivan Science Center 101, UNC Greensboro.

Penny Haxell (U. Waterloo) Matchings in hypergraphs
Jeff Kahn (Rutgers),  Thresholds and "thresholds"
Greta Panova (U. Penn),  Lattice models and symmetric functions
Peter Winkler (Dartmouth),  Permutons

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 U.S. citizens, and what is available to others still requires that the participants be employed at a U.S. university. To request funding please fill out the form here.

Logistical information: The closest airport is Piedmont Triad, which is 10 miles from the university. Other possible airports are Charlotte Douglas (100 miles) or Raleigh-Durham (66 miles). We recommend the Biltmore hotel in downtown Greensboro (1 mile from campus) or the Courtyard Marriott on Wendover Avenue (7 miles from campus). There are many other decent hotels along I-40 a few miles south of campus. We would appreciate if you could go ahead and make your own reservations.

Preregistered Participants (so far):
Alie Alhajjar, George Mason U.
Ed Allen, Wake Forest
Khalid Almnesi, Morgan State U.
Abdullah Alqarni, Morgan State U.
Zeinab Bandpey, Morgan State U.
Emily Barnard, NCSU
Karthik Chandrasekhar, U Kentucky
Jue Cheng, Wake Forest
Greg Clark, USC
Ruth Davidson, UIUC
Brian Davis, U Kentucky
David Galvin, Notre Dame
Anant Godbole, ETSU
Jerry Griggs, USC
He Guo, Georgia Tech
Joshua Hallam, Wake Forest U.
Arran Hamm, Winthrop U.
Penny Haxell, U. Waterloo
Patricia Hersh, NCSU
Gabor Hetyei, UNC Charlotte
Shilpa Jayarajan, Wake Forest
Ashley Jones, UNC Greensboro
Jeff Kahn, Rutgers
Lauren Keough, Davidson College
Julie Lang, USC
Ricky Liu, NCSU
Sarah Mason, Wake Forest
Olsen McCabe, U Kentucky
Thomas McConville, MIT
Marie Mickley, Wake Forest
Michael Mossinghoff, Davidson
Greta Panova, U Penn
Gabor Pataki, UNC Chapel Hill
Josiah Reiswig, USC
Aaron Shank, UNC Greensboro
Michael Singer, NCSU
Caprice Stanley, NCSU
Michael Strayer, UNC Chapel Hill
Spencer Saunders, USC
Anton Strizhov, USC
Seth Sullivant, NCSU
Cliff Smyth, UNC Greensboro
Rupei Xu, UT Dallas
Zhiyu Wang, USC
Hays Whitlatch, USC
Peter Winkler, Dartmouth

Organizing committee: Clifford Smyth, chair (UNC Greensboro), David Galvin (Notre Dame), and Patricia Hersh (NCSU)

Talk titles and abstracts:

Penny Haxell (U. Waterloo)

Title: Matchings in hypergraphs

Abstract: A matching in a hypergraph is a set of disjoint edges. It is a well-known difficult problem to give good lower bounds on the maximum size of a matching in a hypergraph in terms of other natural parameters. Here we discuss tools for this, with a focus on the special case of tripartite hypergraphs: those for which the vertex set can be partitioned into three parts, such that each edge contains exactly one vertex from each part. For example, if a tripartite hypergraph is r-regular (meaning that each vertex is in exactly r edges) with n vertices in each class then it has a matching of size at least n/2, and this is tight for certain special hypergraphs. We investigate how this bound can be improved for all other hypergraphs.

Jeff Kahn (Rutgers)

Title: Thresholds and "thresholds"

Abstract: For a family F of subsets of a finite set X, we're interested in understanding when a "p-random" subset Y of X (gotten by retaining elements independently with probability p) is likely to lie in F. Traditionally one takes F to be increasing (closed under taking supersets), in which case the probability that Y belongs to F increases with p, but there are also many natural families that don't quite fit this framework. We'll try to give some feel for this subject and mention some of the recent progress, or lack thereof.

Greta Panova (U. Penn)

Title: Lattice models and symmetric functions

Abstract: We will discuss lattice models arising from statistical mechanics: lozenge tilings (dimer covers of a hexagonal lattice/plane partitions in special cases), 6-vertex model, dense loop model. They are rich in combinatorial and probabilistic properties. We will describe their limiting behavior as the lattice size goes to 0 and see the arising phenomena -- limit shapes (surfaces), arctic circles, distributions from Random Matrices near the boundary. Proving such probabilistic properties brings in yet another field in play. It can be done with some asymptotic analysis of symmetric functions -- objects from representation theory and algebraic combinatorics, and related combinatorial models of Young tableaux, plane partitions and Gelfand-Tsetlin schemes. Thanks to these methods, we can also consider lozenge tilings with various global symmetries and recover the same probabilistic behavior.

Peter Winkler (Dartmouth)

Title: Permutons

Abstract: Permutons are limit objects for permutations---technically, a permuton is a probability measure on the unit square with uniform marginals. By finding a permuton that maximizes a certain integral, we (with Rick Kenyon, Dan Kral and Charles Radin) can (sometimes) count and describe large permutations that satisfy certain properties---for example, permutations that have specified pattern densities.

Past meetings:

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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