TITLE: Matroids and graphs in surfaces.
ABSTRACT:

A matroid is a mathematical structure that generalises the notion of linear independence in vector spaces. There is a natural way to associate a matroid with a graph, and this results in a very close connection between graph theory and matroid theory. This is beneficial in two ways: graph theory can serve as an excellent guide for studying matroids; and matroid theory can lead to new, and more general, results about graphs. In fact, matroid theory may be best thought of as a generalisation of graph theory.