Geometric representation of graphs and graph minors

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Graphs are used to model information arising from many fields such as economics, engineering, social sciences, genetics, mathematics and computer science. As such, many practical applications require them to be visualized or drawn in ways that are easy to read and understand, or to be layed out in a way that satisfies some physical constraint. The main goal of this project is to study such graph representations. In particular, we propose to study rich connections between the structural, geometric, and topological properties of graphs and apply them to fundamental problems about graph representations (such as graph drawings in two and three dimensions, and embeddings of graphs on surfaces). The structural properties of graphs that will play the key roll in the study are those that arise from the celebrated Graph Minors Theory of Robertson and Seymour.