Triangle Lectures in Combinatorics (TLC)
Sixth meeting: September 22, 2012 at NCSU


Allen Knutson (Cornell): The poset of T.leaves on flag manifolds and wonderful compactifications

Vin de Silva (Pomona College): Circles and co-circles: algebraic topology in data analysis

Richard Stanley (MIT): The visibility arrangement and line shelling arrangement of a convex polytope

Lauren Williams (UC Berkeley): Combinatorics of KP solitons from the real Grassmannian


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

10-11am, Vin de Silva, Pomona College

11-11:30am, coffee break

11:30am-12:30pm, Richard Stanley, MIT

12:30-2:30pm, lunch break

2:30-3:30pm, Allen Knutson, Cornell

3:30-4pm, coffee break

4-5pm, Lauren Williams, Berkeley

Note: there will also be a Friday afternoon NCSU math department colloquium in SAS Hall 2203 at 4pm by Rebecca Goldin on ``Should you believe it? A mathematical perspective on the science of news'' as well as an informal dinner for TLC participants afterwards. There will also be a departmental tea on Friday at 3:30pm in SAS Hall 4104. These events may be a nice gathering place for conference participants on Friday afternoon/evening.

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,, 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 upper right of the map, just left of the star marking the Visitor Info Booth, and its parking lot is a large one shaded red on the map. A good back-up option for parking is the Coliseum Parking Deck (yellow).

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). We especially recommend the Doubletree, or the Cameron Park. 1.5 miles away in downtown Raleigh (also walkable, but somewhat long walk) is the Clarion Raleigh Hotel (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.

Talk titles and abstracts (received so far):

Allen Knutson, The poset of T.leaves on flag manifolds and wonderful compactifications

Abstract: One natural source of stratified spaces is manifolds with torus actions and Poisson structures, where the strata are the T-invariant Poisson subvarieties. The basic example (to serve as a building block) is a Bruhat cell BvB/B in a flag manifold, where the poset of strata is the Bruhat interval [1,v].

I'll describe two families of examples: generalized flag manifolds G/P and wonderful compactifications K-bar of groups. In each case the finite poset of strata embeds into the Bruhat order of an infinite Weyl group (and thus has nice properties, e.g. being EL-shellable). The premier example is G/P a finite-dimensional Grassmannian, whose positroid stratification is indexed by bounded juggling patterns, which sit in the affine Weyl group.

This work is joint with Xuhua He and Jiang-Hua Lu.

Richard Stanley, The visibility arrangement and line shelling arrangement of a convex polytope

Abstract: Let P be a convex polytope, and let x be a point in the interior of P. We define hyperplane arrangements V(P) and L(P,x), called the visibility arrangement and line shelling arrangement of P. The regions of V(P) correspond to sets of facets of P visible from some point. The regions of L(P,x) correspond to line shellings of P from the point x. If x is "generic," then the matroid defined by L(P,x) is the Dilworth truncation of that matroid defined by V(P). We discuss some special cases, some further aspects, and some generalizations of these observations.

Lauren Williams, Combinatorics of KP solitons from the real Grassmannian

Abstract: Given a point A in the real Grassmannian, it is well-known that one can construct a soliton solution u_A(x,y,t) to the KP equation. The contour plot of such a solution provides a tropical approximation to the solution when the variables x, y, and t are considered on a large scale and the time t is fixed. I will describe joint work with Yuji Kodama on the combinatorics of such contour plots. Using the positroid stratification and the Deodhar decomposition of the Grassmannian (and in particular the combinatorics of Go-diagrams), we completely describe the asymptotics of these contour plots when |y| or |t| go to infinity. Other highlights include: a surprising connection with total positivity and cluster algebras; results on the inverse problem; and the characterization of regular soliton solutions -- that is, a soliton solution u_A(x,y,t) is regular for all times t if and only if A comes from the totally non-negative part of the Grassmannian. No background on the KP equation or the Grassmannian will be required.

Preregistered participants (so far):

Taylor Allison, UNC Chapel Hill
Justin Allman, UNC Chapel Hill
Ala'a Al-Kateeb, NCSU
Camilla Smith Barnes, Sweet Briar College (VA)
Jonathan Beagley, George Mason University (VA)
Julie Beier, Mercer University (GA)
Sarah Birdsong, UNC Charlotte
Jonah Blasiak, U. Michigan (MI)
Brandon Bock, NCSU
Brice Boyer, NCSU
Matthew Brown, Virginia Tech (VA)
Patricia Brown, Armstrong University (GA)
Y Timothee Bryan, NCSU
Yue Cai, U. Kentucky (KY)
Chiwei Chao, Clemson (SC)
Manoj Chari, SAS
Shaoshi Chen, NCSU
Ruth Davidson, NCSU
Rob Davis, U. Kentucky (KY)
Graham Enos, UNC Charlotte
Alex Fink, NCSU
Jennifer Gamble, NCSU ECE Department
Shanzhen Gao, UNC Charlotte
Hamza Ghadyali, Duke
Nicole Gin, NCSU
Rebecca Goldin, George Mason University (VA)
Brent Gorbutt, George Mason University (VA)
Darij Grinberg, MIT (MA)
Ruth Haas, Smith College (MA)
Taylor Harrison, NCSU
Qijun He, Clemson (SC)
Patricia Hersh, NCSU
Gabor Hetyei, UNC Charlotte
Jonathan Hauenstein, NCSU
John Hutchens, NCSU
JiYoon Jung, Marshall University (WV)
Yonggu Kim, NCSU
Chris Kirkland, NCSU
Allen Knutson, Cornell (NY)
John Konvalina, University of Nebraska at Omaha (NE)
Hamid Krim, NCSU ECE
Andre Kuney, NCSU
Shirley Law, NCSU
Nan Li, MIT (MA)
Matthew Macauley, Clemson (SC)
Chris Manon, George Mason University (VA)
Sarah Mason, NCSU
Emily Meehan, NCSU
Leonardo Mihalcea, Virginia Tech (VA)
Jed Mihalisin
Ezra Miller, Duke
Kailash Misra, NCSU
Sayan Mukherjee, Duke statistics department
Swarnava Mukhopadhyay, UNC Chapel Hill
Elizabeth Munch, Duke
Vidit Nanda, Rutgers (NJ)
Sarah Nelson, U. Kentucky (KY)
Elizabeth Niese, Marshall University (WV)
Asamoah, Nkwanta, Morgan State University (MD)
Matthew O'Meara, UNC Chapel Hill
Daniel Orr, UNC Chapel Hill
Lindsay Piechnik, High Point University
Shira Polster, NCSU
Svetlana Poznanovik, Clemson (SC)
Bob Proctor, UNC Chapel Hill
Nathan Reading, NCSU
Carla Savage, NCSU
Robert Seay, NCSU
Alan Sheridan, NCSU
Farbod Shokrieh, Georgia Tech (GA)
Vin de Silva, Pomona College (CA)
Sean Skwerer, UNC Chapel Hill, Operations Research Dept
Richard Stanley, MIT (MA)
John Steenbergen, Duke
Ernie Stitzinger, NCSU
Seth Sullivant, NCSU
Ryan Vinroot, College of William and Mary (VA)
Mirko Visontai, Penn (PA)
Weikun Wang, NCSU
Matt Watson, NCSU
Adam Wilkerson, NCSU ECE
Lauren Williams, Berkeley (CA)
Andrew Willis, Virginia Tech (VA)
Matt Willis, Hampden-Sydney College (VA)
Rika Yatchak, NCSU
Taedong Yun, MIT (MA)
Chi Zhang, Duke

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