Last updated Fri 4/17/26
Friday 1/23
Organizational meeting
Friday 1/30
Linus Setiabrata (MIT)
Double Orthodontia Formulas and Lascoux Positivity
Friday 2/6
Reuven Hodges
Comparability in Bruhat Orders
Abstract: I will talk about how my collaborators and I got a tight asymptotic bound for the number of comparable pairs in weak Bruhat order using tools from linear extensions, Plancherel measure, and RSK.
Friday 2/13
Marge Bayer
Flag Vectors of Polytopes
Friday 2/20
Han Yin
The Record Statistic and Forward Stability of Schubert Products
Friday 2/27
Jeremy Martin
Graph Varieties
Abstract: A graph variety is a space whose points parametrize "pictures" of a graph \(G\): arrangements of points and lines with incidence constraints given by \(G\). These spaces turn out to have lots of structure, both geometrically (the component structure is controlled by rigidity properties of the graph), algebraically (the defining equations are certain generating functions for trees), and topologically (the homology groups are determined by the Tutte polynomial). It has been several years since I studied these things in my PhD dissertation, but I will give an overview of what I know about them and the tools that come into play.
Friday 3/6
Jeremy Martin
Graph Varieties II
Abstract: Draw \(n\) distinct points in the plane and connect them with \(\binom{n}{2}\) lines. What are the constraints on the slopes of these lines? The theoery of graph varieties is a starting point for this problem, and there are several unexpected combinatorial phenomena that show up in the algebraic geometry: spanning tree enumeration, noncrossing matchings....
Friday 3/13
Andrés Molina
Oriented Matroids
Friday 3/20
No seminar (Spring Break)
Friday 3/27
No seminar (Graduate Student Combinatorics Conference)
Friday 4/3
David Carlip
Counting Maximal/Maximum Independent Sets
Abstract: A question on the Hilbert-Samuel multiplicity of edge ideals of graphs leads us to consider the maximum number of maximum independent sets in a graph of a fixed order. This is a well-studied question in a variety of classes of graphs, first explored in a result by Moon and Moser in 1965. We will describe their result, as well as similar results on particular classes of graphs. We will then discuss more recent results in counting maximum independent sets for graphs with a fixed independence number.
Friday 4/10
Jeremy Martin
Graph Varieties III
Abstract: This time, I'll go back to focusing on the space of all pictures of an arbitrary graph, in particular the problem of determining its homology groups. The answer turns out to involve the Tutte polynomial, of which I will not assume previous knowledge.
Friday 4/17
Reuven Hodges
Schubert Calculus
Abstract: Schubert calculus is a branch of algebraic geometry concerned with enumerative problems on flag varieties and Grassmannians, rooted in the 19th-century work of Hermann Schubert on counting geometric configurations satisfying prescribed incidence conditions. The modern formulation places these problems within the cohomology ring of a flag variety, where Schubert classes form a natural basis and intersection numbers capture the solutions to classical enumerative questions. In this talk, we explore the foundations of Schubert calculus from two complementary angles: a geometric perspective through the study of Schubert varieties and their intersections, and a combinatorial perspective through symmetric functions, permutation combinatorics, and the Littlewood–Richardson rule.
Friday 4/24
Chris Uchizono
Coxeter Frieze Patterns
Abstract: In the early 1970s, Coxeter studied arrays of numbers known as frieze patterns as a means of exploring Gauss' formulae for pentagramma mirificum. Together with Conway, he discovered that frieze patterns of positive integers correspond to triangulations of regular n-gons, giving rise to combinatorial interpretations. More general frieze patterns have been shown to be related to Auslander-Reiten quivers, cluster algebras, and Grassmannians. Following Sophie Morier-Genoud's survey on the topic, this talk will introduce frieze patterns and their core properties, highlighting their elegant connections across algebra, combinatorics, and geometry.
Friday 5/1
Dan Guyer (University of Washington)
Partitionability for the cd-Index
Abstract: Face enumeration of simplicial complexes is a central topic in geometric combinatorics, and partitionability is a key combinatorial tool to study the associated \(f\)-vector. For objects like polytopes and regular CW spheres, one may wish to not only count the number of faces of each dimension but also keep track of all chains of faces. The flag \(f\)-vector records all possible chains of faces. In its most concise form, the flag \(f\)-vector is expressed via the cd-index, defined by Fine and Bayer--Klapper. In this talk, I will discuss how the concept of partitionability can be extended to study the cd-index. Namely, I will define the class of \(S\)-partitionable posets, demonstrate how they generalize (Eulerian) partitionable simplicial complexes, and illustrate how they admit a recursive combinatorial decomposition that allows one to compute a nonnegative cd-index. This is based on recent joint work with Felipe Caster and José Samper.
Friday 5/8
TBA (Stop Day)
For seminars from previous semesters, please see the KU Combinatorics Group page.
Last updated Fri 4/17/26