Triangle Lectures in Combinatorics (TLC)
Tenth meeting: October 4, 2014

Location: High Point University in High Point, North Carolina (one hour west of the Research Triangle by car).

Lecture Hall: 206 Cogdon Hall MAP (The map also contains parking information.)

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)

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 funding: We have funds available for travel and hotel for participants, especially for early career participants, thanks to grants from the NSF and the NSA. Much of this is restricted to U.S. citizens and permanent residents, and what is available to others still requires that the participants be employed at a U.S. university. To apply for funding fill out the form here: Travel Funding Request Form If you have questions, please contact Nathan Reading (

Saturday Triangle Lectures in Combinatorics Schedule:

9:15-10am, coffee and bagels
10-11am, Rob Ghrist, Poincare Duality in Network Flow Optimization
11-11:30am, coffee break
11:30am-12:30pm, Luis Serrano, The immaculate basis of the non-commutative symmetric functions
12:30-2:30pm, lunch break
2:30-3:30pm, Rekha Thomas, The Euclidean distance degree of an algebraic variety
3:30-4pm, coffee break
4-5pm, Richard Ehrenborg, Euler enumeration
6pm, somewhat informal conference dinner at Sumela

Logistical information: The nearest airport is Greensboro/High Point (GSO), 20 minutes drive away. This is also known as the Piedmont Triad Airport. Within 90 minutes drive are both Raleigh-Durham (RDU) Airport and Charlotte (CLT) Airport. A cab from GSO costs about $30 each way. Hotels are about 1.5 to 3 miles from campus. Thus, a car rental may make sense for anyone flying to the meeting.

A block of hotel rooms has been reserved at the Courtyard Marriott High Point (336-882-3600), which is 1.7 miles from campus. The rooms are blocked off under "The TLC" until September 19th. However, if rooms are still available, they will honor our group rate of $119 per night (+tax) after this date. (The room includes two queen beds, wireless internet, and either a hot breakfast sandwich or two continental breakfast items, plus beverage, for 2 adults). There are many other local options including: -High Point Plaza , 1 mile from campus (more downtown). 336-889-8888 -Crestwood Suites, about 2.7 miles from campus (more economical). 336-886-5665.

Preregistered Participants (so far):

Geir Agnarsson, George Mason University
Ed Allen, Wake Forest
Taylor Allison, UNC Chapel Hill
Justin Allman, Virgina Tech
Jennifer Anderson, Marshall University
Emily Barnard, NCSU
Yue Cai, U Kentucky
Dustin Cartwright, U Tennessee
Shihwei Chao, Clemson University
Paul Cubre, Clemson University
Brian Davis, U Kentucky
Robert Davis, U Kentucky
Rafael S. Gonzalez D'Leon, U Kentucky
Anahita Davoudi, U Central Florida
Vivek Dhand, Charlottesville, VA
Richard Ehrenborg, U Kentucky
Norman Fox, U Kentucky
Amy Grady, Clemson University
Rob Ghrist, U Penn
Alex Happ, U Kentucky
Isaiah Harney, U Kentucky
Qijun He, Clemson
Patricia Hersh, NCSU
Qijun He, Clemson University
Cyrus Hettle, U Kentucky
Gabor Hetyei, UNC Charlotte
Elliot Hollifield, Wake Forest U
Chetak Hossain, NCSU
Wesley Hough, U Kentucky
Andy Jenkins, Clemson University
Yvonne Kemper, NIST
Florian Kohl, U Kentucky
Rebecca Kotsonism, Wake Forest U
David Lax, UNC Chapel Hill
David Mason, UNC Chapel Hill
Sarah Mason, Wake Forest
Marie Meyer, U Kentucky
Frank Moore, Wake Forest U
John Mosley, U Kentucky
Sayan Mukherjee, Duke
Vidit Nanda, U Penn
Yusra Naqvi, Rutgers
Sarah Nelson, U Kentucky
Elizabeth Niese, Marshall University
Jason Parsley, Wake Forest U
Gabor Pataki, UNC Chapel Hill
Svetlana Poznanovikj, Clemson U
Sarah Orchard, U Kentucky
Lindsay Piechnik, High Point
Richard Rimanyi, UNC Chapel Hill
Radmila Sazdanovic, NCSU
Luis Serrano, UQAM
Cliff Smyth, UNC Greensboro
Liam Solus, U Kentucky
Jeremiah Southwich, Wake Forest U
Kara Stasikelis, Clemson University
Seth Sullivant, NCSU
Breeanne Swart, The Citadel
Clifford Taylor, U Kentucky
Rekha Thomas, U Washington
Tzvetalin Vassilev, Nippising U.
Devin Wilmott, U Kentucky
Martha Yip, U Kentucky
Laurie Zack, High Point

Talk titles and abstracts:

Richard Ehrenborg (U Kentucky)

Title: Euler enumeration

Abstract: The flag vector contains all the face incidence data of a polytope, and in the poset setting, the chain enumerative data. It is a classical result due to Bayer and Klapper that for face lattices of polytopes, and more generally, Eulerian graded posets, the flag vector can be written as a cd-index, a non-commutative polynomial which removes all the linear redundancies among the flag vector entries. This result holds for regular CW complexes. We relax the regularity conditions to show the cd-index exists for manifolds whose boundary has a Whitney stratification. The setting of Whitney stratifications allows us to give shorter proofs of identities involving the cd-index and opens inequality questions for manifolds. This is joint work with Mark Goresky and Margaret Readdy.

Rob Ghrist (U Pennsylvania)

Title: Poincare Duality in Network Flow Optimization

Abstract: One of the classical cornerstones of optimization theory is LP (linear programming) duality, and one of its simplest applications is to the classical max-flow-min-cut theorem, which expresses a duality between optimal network flow values and optimal cut capacities. This talk argues that flow-cut duality is really topological in nature -- an expression of Poincare duality. A recent proof by S. Krishnan shows that Poincare duality on sheaves of semimodules implies a sheaf-theoretic extension of the classical max-flow-min-cut theorem. This greatly expands the types of problems to which flow-cut dualities can be applied, as well as explains the source of duality gaps in more advanced settings. This talk will give details.

Luis Serrano (U Quebec a Montreal)

Title: The immaculate basis of the non-commutative symmetric functions

Abstract: We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions and decompose Schur functions according to a signed combinatorial formula. These bases have many interesting properties similar to those of the Schur basis, and we will outline a few of them.

Rekha Thomas (U Washington)

Title: The Euclidean distance degree of an algebraic variety

Abstract: It is a common problem in optimization to minimize the Euclidean distance from a given data point u to some set X. In this talk I will consider the situation in which X is an algebraic variety, a common situation in practice. The number of critical points of the objective function on X is called the Euclidean distance degree of X, and is an intrinsic measure of the complexity of this polynomial optimization problem. Using algebraic geometry we obtain formulas and methods to calculate this degree in many situations. I will explain the results and illustrate the formulas that can be obtained in several situations ranging from matrix analysis to control theory to computer vision. Joint work with Jan Draisma, Emil Horobet, Giorgio Ottaviani and Bernd Sturmfels.