University of Kentucky Discrete CATS Seminar
U N I V E R S I T Y   O F   K E N T U C K Y


2018 -- 2019

Fall 2018

Unless otherwise noted, seminar meets at 2:00 pm Mondays in 745 POT.

Sept 10 Richard Ehrenborg
University of Kentucky
Uniform flag triangulations of the Legendre polytope (or how I spent my summer holiday)

The Legendre polytope, also known as the full root polytope of type A, is the convex hull of all pairwise differences of the basis vectors. We describe all flag triangulations of this polytope that are uniform, that is, the edges are described in terms of the relative order of the indices of the four basis vectors involved. We obtain three classes of triangulations: the lex class, the revlex class and the Simion class. We also do a refined enumeration of faces of these triangulations that keeps track of the number of forward and backward arrows, and surprisingly the enumeration result only depends on which class the triangulation belongs to.

Joint work with Gabor Hetyei and Margaret Readdy.

Sept 17 Margaret Readdy
University of Kentucky
Combinatorial identities related to the calculation of the cohomology of Siegel modular varieties

In the computation of the intersection cohomology of Shimura varieties, or of the L2 cohomology of equal rank locally symmetric spaces, combinatorial identities involving averaged discrete series characters of real reductive groups play a large technical role. These identities can become very complicated and are not always well-understood. We propose a geometric approach to these identities in the case of Siegel modular varieties using the combinatorial properties of the Coxeter complex of the symmetric group

Joint work with Richard Ehrenborg and Sophie Morel.

Oct 1 Ben Braun
University of Kentucky
Graph constructions and chromatic numbers
We will survey various graph constructions related to proper k-colorability. Possible topics for discussion include constructions of k-chromatic graphs due to Hajos, Ore, and Urquhart, constructions of graphs with high girth and high chromatic number due to Alon, Kostochka, Reiniger, West, and Zhu, and constructions of k-critical graphs with minimal possible number of edges due to Kostochka and Yancey.

Oct 8 Matthias Köppe
UC Davis
Normalized antics: Polyhedral computation in an irrational age
Classic polyhedra such as the dodecahedron have irrational coordinates. How do we compute with them if we need exact answers? In this hands-on lecture using the SageMath system, intended to be accessible to advanced undergraduate students, I explain how to compute with polyhedral representations and with real embedded algebraic number fields. I then report on an ongoing project with W. Bruns, V. Delecroix, and S. Gutsche to obtain an efficient implementation in Normaliz, integrated with SageMath, involving the existing software libraries ANTIC, arb, and FLINT.

Oct 15

Alex Chandler
NC State
Thin posets and homology theories
Inspired by Bar-Natan's description of Khovanov homology, we discuss thin posets and their capacity to support homology and cohomology theories which categorify rank-statistic generating functions. Additionally, we present two main applications. The first, a categorification of certain generalized Vandermonde determinants gotten from the Bruhat order on the symmetric group by applying a special TQFT to smoothings of torus link diagrams. The second is a broken circuit model for chromatic homology, categorifying Whitney's broken circuit theorem for the chromatic polynomial of graphs.

Oct 22 No meeting Robert Lang Origami workshop 2-5 pm

Oct 29 Ricky Liu
NC State

Nov 5 No meeting Hayden-Howard Lecture 4 pm

Nov 12 Yuan Zhou
U Kentucky

Nov 19 Fernando Shao
U Kentucky

Nov 26 Tefjol Pllaha
U Kentucky
Laplacian Simplices II: A Coding Theoretic Approach
This talk will be about Laplacian simplices, that is, simplices whose vertices are rows of the Laplacian matrix of a simple connected graph. We will focus on graphs and graph operations that yield reflexive Laplacian simplices. We spot such graphs by showing that the h*-vector of the simplex is symmetric. We use the same approach as Batyrev and Hofscheier by considering the fundamental parallelepiped lattice points as a finite abelian group. This is joint work with Marie Meyer.

Dec 3 Open Date

Seminar Archive

Margaret Readdy is the organizer of the Discrete CATS Seminar. If you wish to be added to the seminar list or give a talk, please e-mail her at margaret.readdy (at)

We would like to thank Richard Ehrenborg (Simons Foundation Collaboration Grant 2016--2021), Margaret Readdy (Simons Foundation Collaboration Grant 2016--2021) and Martha Yip (Simons Foundation Collaboration Grant 2016--2021) who generously continue to support our speakers with their grants. The Discrete CATS seminar is partially supported by the University of Kentucky Department of Mathematics.

Last updated October 7, 2018.