Event Details

Templates for Representable Matroids

The matroid structure theory of Geelen, Gerards, and Whittle has led to an announced result that the highly connected members of certain minor-closed class of matroids representable over a finite field are mild modifications (known as perturbations) of frame matroids, which generalise graphic matroids. They introduced the notion of a template to describe these perturbations in more detail. In this talk, we will define templates and discuss how templates are related to each other. We use templates to obtain results about representability, extremal functions, and excluded minors for various minor-closed classes of matroids. These classes include the class of golden-mean matroids and some closely related classes of matroids representable over the field of four elements.