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

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.

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.

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.

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