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.

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

**Location:** Sullivan Science Center 101, UNC Greensboro.

**Speakers:**

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 plhersh@ncsu.edu
(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.

**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**