| Many real-world problems can be modeled by networks (graphs) and matrices. Algorithms for such problems often rely on an insightful visualization of the model: on an embedding in a space we understand, like a particular topological or linear space. So it is important that we can test efficiently if the graph or matrix has such advantageous appearance. This requires a structural study of the graphs or matrices at hand. For graphs this has been the famous and deep Robertson Seymour Graph Minor Project. One of its major outcomes is that minor closed graph properties can be verified efficiently. This required a deep understanding of the structure of so called minor closed classes of graphs. Over the last couple of years Geelen (University of Waterloo, Canada), Gerards (CWI Amsterdam and TU Eindhoven), and Whittle (Victoria University, Wellington, New Zealand) carry out the same program, but now for matrices over finite fields. Concrete objects of study here are matroids; they abstract the relevant combinatorial properties of matrices. The current project proposal fits into this program. Its main goal is to enhance understanding of the interaction between structure and algorithms for minor closed classes of matroids. |
