Caitlin Mitchell: Excluded minors of swirl matroids

Abstract: Swirls arose in matroid theory as counterexamples to a Kahn’s conjecture regarding representability, a fundamental matroid theory problem. As in graph theory, excluded minors are used to characterise classes of matroids. In this seminar we will look at a an excluded minor problem in matroid theory, namely finding the complete list of excluded minors for a class of matroids called the swirl minors. First we will motivate the problem and introduce some basic definitions, and then explore approaches to completing the list.