Recent research has pointed to fundamental underlying relationships between each of three sub-fields of combinatorics: matroid theory, structural graph theory, and topological graph theory. While the connection between matroids and graphs is long-established, newer foundational links with topological graph theory are creating fresh opportunities for cross-disciplinary advances. The purpose of this workshop is to provide the first dedicated forum to bring together experts in all these three fields to share techniques and approaches, and seed ongoing cross-disciplinary collaboration and advances.