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 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), Scott Provan (UNC Chapel Hill), and Nathan Reading (NCSU)





Next meeting: September 22, 2012 at NCSU

Speakers: Allen Knutson (Cornell), Vin de Silva (Pomona College), Richard Stanley (MIT), and Lauren Williams (UC Berkeley)

Lecture Hall: SAS Hall 1102, NCSU

Schedule:

9:15-10am, coffee, tea and bagels (just outside SAS 1102)

10-11am, TBA

11-11:30am, coffee break

11:30am-12:30pm, TBA

12:30-2:30pm, lunch break

2:30-3:30pm, TBA

3:30-4pm, coffee break

4-5pm, TBA

Participant support: we now have financial support available for participants, thanks to NSF and NSA. To apply for funding for hotel and mileage or airfare, send email to Patricia Hersh, plhersh@ncsu.edu, including the following: (1) estimated hotel expense, (2) roundtrip driving mileage or estimated airfare, and (3) a sentence or two of justification of why it will be valuable to you to attend the meeting.

Practical details:

Parking: You may park right outside SAS Hall for free. Here is a map of the campus with parking lots marked. 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 right of the map, just left of the compass, and its parking lot is a large one shaded red on the map. A good back-up option for parking is the Colliseum 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: within short walk of the math department are three hotels: Doubletree by Hilton Raleigh - Brownstone (919-828-0811), Velvet Cloak Inn (919-828-0333) and Cameron Park Inn Bed and Breakfast (919-835-2171). Those with cars might also consider hotels farther away such as various choices on Wake Town Drive, which is near numerous good restaurants; some such hotels (all right next to each other) 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.

Preregistered participants (so far):

Camilla Smith Barnes, Sweet Briar College
Shaoshi Chen, NCSU
Ruth Davidson, NCSU
Rob Davis, U. Kentucky
Alex Fink, NCSU
Patricia Hersh, NCSU
John Hutchens, NCSU
Allen Knutson, Cornell
Nan Li, MIT
Ezra Miller, Duke
Kailash Misra, NCSU
Nathan Reading, NCSU
Carla Savage, NCSU
Vin de Silva, Pomona College
Sean Skwerer, UNC Chapel Hill, Operations Research Dept
Richard Stanley, MIT
Lauren Williams, Berkeley

Organizing committee: Alex Fink (NCSU), Patricia Hersh (NCSU) and Carla Savage (NCSU)





Recent Spring 2012 meeting: February 11, 2012 at Duke University


Speakers: Alex Fink (NCSU), Matroid Valuations; Sergey Fomin (Michigan), Cluster structures in rings of SL_3 invariants; Nets Katz (Indiana University), Erdos Distinct Distances problem in the plane; and Isabella Novik (University of Washington), Face numbers of centrally symmetric polyopes.

Location: Talks will be in Physics Building Room 128, with coffee breaks in Physics Building Room 101, both at Duke University, Durham, NC

Parking: available in the Bryan Center Parking Garage (PG4) for $5 for the day. This is across the street from the Physics Building.

Schedule:

Friday 4-5pm, NCSU Algebra and Combinatorics Seminar: Leo Mihalcea, Curve Neighborhoods of Schubert Varieties, SAS Hall 4201, NCSU (Raleigh, NC)

Friday 6pm, Seminar Dinner, Details to be determined at the seminar

Saturday, 9:15-10am: coffee and bagels

10-11am, Nets Katz, Erdos Distinct Distance Problem in the Plane

11-11:30am, coffee break

11:30am-12:30pm, Alex Fink, Matroid Valuations

12:30-2:30pm, lunch break

2:30-3:30pm, Isabella Novik, Face Numbers of Centrally Symmetric Polytopes

3:30-4pm, coffee break

4-5pm, Sergey Fomin, Cluster Structures in Rings of SL_3 Invariants

6pm-??, Conference dinner at Revolution, located at 107 West Main Street (with street parking and nearby parking garage).


To preregister: send email to Patricia Hersh, plhersh@ncsu.edu (there is no registration fee).

Participant expense reimbursement: There is some limited funding available to reimburse participant hotel and mileage expenses -- if this would help you to be able to attend, please send email to Patricia Hersh, plhersh@ncsu.edu, to apply for funding. Include in this email (1) expected hotel expense for 1-2 nights, (2) total roundtrip mileage (or cost of airfare), (3) a sentence or two of justification, (4) list of other sources of funding available to you. This is primarily intended for participants driving a substantial distance or with compelling reasons it would help their research to be able to stay overnight in the Triangle area.

Hotel suggestions:

Hilton Durham, 919-383-8033, 3800 Hillsborough Rd, Durham, NC (rooms for $130 per night)
Millenium Hotel, 919-383-8495, 2800 Campus Walk Ave, Durham, NC (rooms for $130 per night)
Brookwood Inn, 877-616-2306, 2306 Elba St, Durham, NC (rooms for $100 per night)


Talk titles and abstracts:

Speaker:Alex Fink

Title:Matroid valuations

Abstract: Many important invariants for matroids, such as the Tutte polynomial, the Billera-Jia-Reiner quasi-symmetric function, Derksen's universal invariant, and Speyer's invariant describing the combinatorics of the Bergman fan, are _valuative_; that is, they are well-behaved under decompositions of the polytopes. I will construct the module of matroid valuations, and describe an explicit combinatorial basis, starting from Brion's theorem; these results can be extended to polymatroids, and there is a natural Hopf algebra structure as well. From a similar starting point, lattice point combinatorics can be used to associate to every matroid a class in the $K$-theory of the Grassmannian. This, in particular, provide an algebro-geometric interpretation of the Tutte polynomial parallel to Speyer's invariant.

Speaker: Sergey Fomin

Title: Cluster structures in rings of SL_3 invariants

Abstract: The rings of polynomial SL(V)-invariants of configurations of vectors and linear forms in a k-dimensional complex vector space V have been explicitly described by Hermann Weyl in the 1930s. Each such ring conjecturally carries a natural cluster algebra structure (typically, many of them) whose cluster variables include Weyl's generators. In joint work with Pavlo Pylyavskyy, we describe and explore these cluster structures in the case k=3.

Speaker: Nets Katz

Title: Erdos Distinct Distances problem in the plane

Abstract: In joint work with L. Guth, we show that there is a universal constant C>0 so that any set of N points in the plane determines at least {N \over C log N} distinct distances. This settles a longstanding problem of Erd\"os regarding the best exponent of N that one can obtain in that estimate.

Speaker: Isabella Novik

Title: Face numbers of centrally symmetric polytopes

Abstract: How neighborly can a centrally symmetric d-dimensional polytope with n vertices be? What is the largest number of i-dimensional faces that such a polytope can have? Which of these polytopes have the largest number of faces? In this talk I'll report on some recent progress (joint with Alexander Barvinok, Seung Jin Lee, and Nati Linial) on these questions.

Preregistered participants:

Geir Agnarsson, George Mason University (Fairfax, VA)
Ed Allen, Wake Forest University (Winston-Salem, NC)
Taylor Allison, NCSU (NC)
Cammie Smith Barnes, Sweet Briar College (Sweet Briar, VA)
Christine Berkesch, Duke University (NC)
Sarah Birdsong, UNC Charlotte (Charlotte, NC)
Yue Cai, University of Kentucky (Lexington, KY)
Shaoshi Chen, NCSU (NC)
Ruth Davidson, NCSU (NC)
Alex Fink, NCSU (NC)
Sergey Fomin, Michigan (Ann Arbor, MI)
Jennifer Gamble, NCSU (NC)
Patricia Hersh, NCSU (NC)
Gabor Hetyei, UNC Charlotte (Charlotte, NC)
JT Hird, NCSU (NC)
Johnny Humphries (NC)
John Hutchens, NCSU (NC)
Naihuan Jing, NCSU (NC)
Garrett Johnson, NCSU (NC)
Austin Jones, NCSU (NC)
JiYoon Jung, University of Kentucky (Lexington, KY)
Nets Katz, Indiana University (Bloomington, IN)
Sangwook Kim, George Mason University (Fairfax, VA)
Yonggu Kim, visiting NCSU from Korea (NC)
Patricia Klein, NCSU (NC)
David Lax, UNC Chapel Hill (NC)
Matthew Macauley, Clemson University (Clemson, SC)
Sonja Mapes, Duke University (NC)
Sarah Mason, Wake Forest University (Winston-Salem, NC)
Leo Mihalcea, Virginia Tech (Blacksburg, VA)
Jed Mihalisin, Meredith College (Raleigh, NC)
Ezra Miller, Duke University (NC)
Kailash Misra, NCSU (NC)
Michael Mossinghoff, Davidson College (Davidson, NC)
Liz Munch, Duke University (NC)
Elizabeth Niese, Marshall University (Huntington, WV)
Asamoah Nkwanta, Morgan State University (Baltimore, MD)
Isaballa Novik, Univ. of Washington (Seattle, WA)
Matthew O'Meara, UNC Chapel Hill (NC)
Lindsay Piechnik, High Point University (High Point, NC)
Nathan Reading, NCSU (NC)
Carla Savage, NCSU (NC)
Seth Sullivant, NCSU (NC)
Ryan Vinroot, College of William and Mary (Williamsburg, VA)
Mirko Visontai, U Penn (Philadelphia, PA)
Weikun Wang, NCSU (NC)
Adam Wilkerson, NCSU (NC)

Organizing Committee: Christine Berkesch (Duke), Sonja Mapes (Duke) and Ezra Miller (Duke)





Past meetings:

Fourth meeting: November 5, 2011 at UNC Chapel Hill
Speakers: Thomas Lam (University of 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 NC State
Speakers: Prakash Belkale (UNC Chapel Hill), Vic Reiner (University of Minnesota), John Stembridge (University of Michigan), Stephanie van Willigenberg (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 NC State
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 (including talk slides)