Fall 2018

- The Combinatorics Seminar meets on Fridays in Snow 408 from 4-5pm.
- Please contact Jeremy Martin or Federico Castillo if you are interested in speaking.
- Good general seminar-attending advice, especially for graduate students: The "Three Things" Exercise for getting things out of talks by Ravi Vakil
- A good general resource (which we may use this semester):
*A Combinatorial Miscellany*by Anders Björner and Richard Stanley

**Friday 8/24**

Organizational Meeting

**Friday 8/31**

Federico Castillo

*What is... Cohen-Macaulayness?*

**Friday 9/7**

Marge Bayer

*Matching Complexes*

**Friday 9/14**

Jeremy Martin

*What is... a combinatorial Hopf algebra?*

**Friday 9/21**

Joseph Doolittle

*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.

**Friday 9/28**

Ken Duna

*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.

**Friday 10/5**

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.

**Friday 10/12**

No seminar (Fall Break)

**Friday 10/19**

Emma Christensen

*What is... a generalized permutohedron?*

**Friday 10/26**

Kevin Marshall

*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.

**Friday 11/2**

No seminar

**Friday 11/9**

Ken Duna

*Fun with the Vertical Strip Conjecture, SNN's, and Truncated Cubes*

**Friday 11/16**

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.

**Friday 11/23**

No seminar (Thanksgiving)

**Friday 11/30**

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)

Joseph Doolittle

*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):

- Dylan - universal algebra
- Emma - generalized permutohedra
- Federico - Cohen-Macaulayness
- Jeremy - root systems, E_8
- Joseph - Grassmannian
- Ken - Cayley graphs
- Kevin - Borel-fixed ideals
- Mark - Polya's theorem

For seminars from previous semesters, please see the KU Combinatorics Group page.

Last updated Fri 11/2/18