What is... Cohen-Macaulayness?
What is... a combinatorial Hopf algebra?
Reconstructing Spheres and Polytopes
Abstract: We investigate the historical progress of the problem of determining all faces of a sphere from partial information, starting in 1916 through the modern day. As we progress through the results, we will also build up the needed tools to understand their proofs, culminating in a counterexample which disproves the strongest possible version of a conjecture made in 1960. While one conjecture falls, it leaves behind a new technique which may solve the crown jewel of this area, that simplicial spheres are reconstructible from their facet-ridge graph.
An Introduction to Graph Spectra
Abstract: I will wax poetic on the spectra of various matrices associated with graphs. As well, we will briefly discuss cospectrality with respect to certain matrices.
Kate Lorenzen (Iowa State University)
Constructions of distance Laplacian cospectral graphs
Abstract: Graphs are mathematical objects that can be embedded into matrices. Two graphs are cospectral if they have the same set of eigenvalues with respect to a matrix. In this talk, we discuss two constructions of cospectral graphs for the distance Laplacian matrix. The first uses vertex twins which have predictable eigenvectors and eigenvalues in the distance Laplacian. The second develops a relaxation of twins called vertex cousins. This second construction produces the only pair of bipartite distance Laplacian cospectral graphs on eight vertices.
No seminar (Fall Break)
What is... a generalized permutohedron?
Security Games on Matroids
Abstract: We consider a game originally played on graphs that easily generalizes to matroids. The game involves two players called Bob and Eve. Simultaneously Bob chooses a basis of a given matroid and Eve chooses a ground set element of the same matroid. Eve wins if she picks an element of Bob's basis otherwise Bob wins. We consider which strategies maximize Bob's chances of winning. The solution to this was shown for the graph case by Gueye, Walrand, and Anantharam in 2011. In 2016 a solution to the more general matroid case was given by Szeszlér.
Fun with the Vertical Strip Conjecture, SNN's, and Truncated Cubes
Jason Clemens (Wichita State University)
Modulus on Graphs with a Focus on Spanning Tree Modulus
Abstract: The concept of conformal modulus was originally developed in complex analysis, but the construction of discrete modulus is quite similar. This talk will focus on the development of the modulus of a family of objects on a graph. With the family of spanning trees, it will be shown that the 2-Modulus problem is related to a number of other interesting problems. For example, through the concept of blocking duality, spanning tree modulus is strongly connected to the modulus of a transverse family of objects, the feasible partitions. The solution to either of these problems immediately yields the solution of the other. From a probabilistic viewpoint, spanning tree modulus is related to problems involving random spanning trees. Finally, this talk will cover a greedy approach to computing spanning tree modulus, and hence gives a solution to all of the related problems.
No seminar (Thanksgiving)
Jay Schweig (Oklahoma State U.)
Toric ideals, Gröbner bases, and Borel ideals, from a combinatorial perspective
Abstract:We discuss toric ideals, which are non-monomial ideals that correspond to the kernel of a natural map between two rings. Although these ideals are typically addressed in an algebraic setting, we'll approach them combinatorially, showing how certain properties (such as having a Gröbner basis) is equivalent to a question about a family of graphs. We will also apply these techniques to certain Borel ideals. This talk will be accessible to graduate students, and I won't assume prior knowledge of any of the objects in the title.
Friday 12/7 (Stop Day)
What is... a Grassmannian?
Tuesday 12/11, 10:30am-1:00pm
Math 824 Project Presentation Day
Here's our potential list of speakers and "What is..." topics (subject to change):
For seminars from previous semesters, please see the KU Combinatorics Group page.
Last updated Fri 11/2/18