YouTube recording: https://youtu.be/UdjhEgSKQus

Time: Thursday, Feb 2, 3pm EST (8pm GMT, 9am Fri NZDT)
Zoom: https://gatech.zoom.us/j/8802082683

Speaker: Tom Zaslavsky, Binghamton University
Title: Matroids of gain signed graphs
Abstract: For standard affinographic hyperplane arrangements (a.k.a. deformations of
the Type A root system arrangement or “braid” arrangement), integral gain
graphs give a simpler method to compute the characteristic polynomial, a
fundamental invariant.  For more general affinographic arrangements
(a.k.a. deformations of the Type B root system arrangement), one has to
combine gains with signs.  How to do this has been a puzzle.  The obvious
method is to put signs on top of gains.  The right method is to put gains
on top of signs.  Laura Anderson, Ting Su, and I found out how to do this,
constructing the natural matroid and the corresponding semimatroid, which
latter gives the characteristic polynomial of these more general
arrangements when the gain group is the additive group of integers.  I
will explain some of this.  It does get complicated.

YouTube recording: https://youtu.be/acJnDJ7sZPM

The online Graphs and Matroids seminar will meet over Zoom every other Thursday, starting on Jan 19 with a talk by Johannes Carmesin. We hope to see you there!

Time: Thursday, Jan 19, 3pm EST (8pm GMT, 9am Fri NZDT)
Zoom: https://gatech.zoom.us/j/8802082683

Speaker: Johannes Carmesin, University of Birmingham
Title: Dual matroids of 2-complexes
Abstract: A fundamental theorem in matroid theory is Whitney’s theorem,
saying that a graph is planar if and only if the dual of its cycle matroid
is graphic. Like plane graphs, 2-complexes C embedded in 3-space have dual
graphs; their vertices are the chambers of the embedding and two chambers
are adjacent if they share a face. This dual graph of C can be described
through a dual matroid of the 2-complex C. How can Whitney’s theorem be
extended to 2-complexes?

Tuesday, April 12, 3pm ET (8pm BST, 7am Wed NZST)
Carolyn Chun, United States Naval Academy
Lattice path matroids, lattice path polymatroids, and excluded minors

Abstract:

We define lattice path matroids, polymatroids, Boolean polymatroids, and lattice path polymatroids, which are a subclass of Boolean polymatroids.  We give an excluded minor characterization for lattice path polymatroids, based on a proof where the main tool was Venn diagrams!  There are infinitely many excluded minors for lattice path polymatroids, but they fall into a small number of easily-described types.

Tuesday, April 5, 3pm ET (8pm BST, *7am* Wed NZST)
Lise Turner, University of Waterloo
A local version of Hadwiger’s Conjecture

Abstract:

In 1943, Hadwiger famously conjectured that graphs with no $K_t$ minors are $t-1$ colourable. There has also been significant interest in several variants of the problem, such as list colouring or only forbidding certain classes of minors. We propose a local version where all balls of radius $O(\log v(G))$ must be $K_t$-minor free but the graph as a whole may not be. We prove list colouring results for these graphs equivalent to the best known results for $K_t$-minor free graphs for $t\leq 5$ and large $t$. In the process, we provide some efficient distributed algorithms for finding such colourings.

Joint work with Benjamin Moore and Luke Postle.