Practical information about hotels, airport, taxis and about parking and information about dining options.

Louis Billera's talk as pdf file

Rod Canfield's talk as pdf file

Matthew Kahle's talk as pdf file

Michelle Wachs' talk as pdf file

9:15-10am, coffee and bagels

10-11am, Louis Billera

11-11:30am, coffee break

11:30am-12:30pm, Rod Canfield

12:30-2:30pm, lunch break

2:30-3:30pm, Matthew Kahle

3:30-4pm, coffee break

4-5pm, Michelle Wachs

Louis Billera (Cornell)

Rod Canfield (University of Georgia)

Matthew Kahle (Ohio State University)

Michelle Wachs (University of Miami)

This should take you 30 seconds or less using the online preregistration form , or a few minutes longer if you apply for funding.

Graduate students and early career mathematicians are particularly encouraged to apply for funding. To apply, use the online preregistration form . We will need the following information: (1) estimated roundtrip mileage and/or airfare and local travel expenses, (2) estimated hotel cost, (3) a sentence or two of justification for why it would be useful for you to participate, and (4) other possible funding sources. Funding decisions will be made shortly after the 15th of each month up until the conference or until all funds have been committed.

Abstract: A collection of nonempty subsets of the set {1,...,n} is said to be balanced if the convex hull of the indicator functions of these sets in the n-cube meets the diagonal. The collection is unbalanced otherwise.

Balanced collections were defined 50 years ago by Lloyd Shapley (who was awarded a Nobel Prize in Economics last December) in his study of cores of cooperative games. Minimal balanced collections played an important role in determining when such games arise from economic trading models. One can view minimal balanced collections as generalized partitions.

Maximal unbalanced collections arose recently in physics in the study of thermal field theory, a combination of quantum field theory and statistical mechanics. They are also closely related to the study of threshold Boolean functions, threshold collections and voting games. We consider a hyperplane arrangement whose regions correspond to unbalanced collections.

I will say a bit about the applications of balanced and unbalanced collections and give relations between the various questions they ask. The talk will be more a survey than a recitation of new results, although some new approaches will be described. In particular, there are many questions here that modern algebraic combinatorics ought to be able to answer.

Abstract: Suppose $a_n$, $n \ge 0$, is a sequence of positive integers of combinatorial interest; typically the $a_n$ count something. The existence of the limit $\lim_{n\rightarrow\infty} (a_n)^{1/n}$ can sometimes be difficult to prove. When the limit is known to exist, there arises the challenge to pinpoint it in some way, for example as the root of a polynomial or transcendental equation. In the study of locally restricted compositions we find many such limits which can be linked to the eigenvalues of infinite matrices. (A composition of $n$ is a $k$-tuple $(c_1,\dots,c_k)$ of positive integers whose sum is $n$; local restrictions are conditions such as ``no two adjacent parts are equal,'' or ``the parts alternate in magnitude.'') Directions for further study will be indicated. This is collaborative research with Ed Bender and Jason Gao.

Abstract: Configuration spaces of points are well-studied spaces in algebraic topology, algebraic geometry, geometric group theory, and combinatorics. Give the particles thickness, and you have what physicists might describe as phase space for a hard spheres gas. When the points are points, the topology of the configuration space is well understood but hardly anything is known when points have thickness. Then changes in the topology as the thickness varies could be thought of as topological phase transitions.

I will report on recent work understanding these kinds of changes in topology, including work in progress with Bob MacPherson.

Abstract: We consider three distinct topics of independent interest; one in enumerative combinatorics, one in symmetric function theory, and one in algebraic geometry. The topic in enumerative combinatorics concerns a q-analog of a generatlization of the Eulerian numbers, the one in symmetric function theory deals with a refinement of Stanley's chromatic symmetric functions, and the one in algebraic geometry deals with a representation of the symmetric group on the cohomology of the regular semisimple Hessenberg variety of type A. Our purpose is to explore some connections between these topics and consequences of these connections. This talk is based on joint work with John Shareshian.

Ed Allen, Wake Forest University

Taylor Allison, UNC Chapel Hill

Fawwaz Batayneh, Clemson

Jonathan Beagley, George Mason University

Kenneth Berenhaut, Wake Forest University

Christine Berkesch, Duke

Louis Billera, Cornell University

Sarah Birdsong, UNC Charlotte

Kayla Blyman, University of Kentucky

Yue Cai, U. Kentucky

Rod Canfield, University of Georgia

Shihwei Chao, Clemson

Shaoshi Chen, NCSU

Ruth Davidson, NCSU

Robert Davis, University of Kentucky

Alex Fink, NCSU

Norman Fox, University of Kentucky

Jennifer Galovich, Virginia Tech

Jennifer Gamble, NCSU

Nicole Gin, NCSU

Rafael S. Gonzelez D'Leon, University of Miami

Brent Gorbutt, George Mason University

Darij Grinberg, MIT

Qijun He, Clemson

Patricia Hersh, NCSU

Gabor Hetyei, UNC Charlotte

John Hutchens, NCSU

Austin Jones, NCSU

Matthew Kahle, Ohio State University

Chris Kirkland, NCSU

Andrey Kuney, NCSU

Shirley Law, NCSU

David Lax, UNC Chapel Hill

Matthew Macauley, Clemson

Sarah Mason, Wake Forest University

Emily Meehan, NCSU

Sam Mendelson, George Mason University

Ezra Miller, Duke

Walter Morris, George Mason University

John Mosley, University of Kentucky

Michael Mossinghoff, Davidson College

Sayan Mukherjee, Duke

Sarah Nelson, University of Kentucky

Asamoah Nkwanta, Morgan State University

Christopher O'Neill, Duke

Elliot Paquette, U. Washington

Lindsay Piechnik, High Point University

Shira Polster, NCSU

Svetlana Poznanovik, Clemson

Scott Provan, UNC Chapel Hill

Nathan Reading, NCSU

Joe Rusinko, Winthrop University

Carla Savage, NCSU

Michael Singer, NCSU

John Steenberger, Duke

Seth Sullivant, NCSU

Clifford Taylor, U Kentucky

Nate Tryon, NCSU

Bethany Turner, NCSU

Hayato Ushijima-Mwesigwa, Clemson

Mirko Visontal, KTH

Michelle Wachs, University of Miami

Rika Yatchak, NCSU