Geometric representation of graphs and graph minors

图用于对来自许多字段的信息进行建模，例如 经济学、工程学、社会科学、遗传学、数学和 计算机科学。因此，许多实际应用要求它们 以易于阅读和理解的方式进行可视化或绘制，或以满足某些物理约束的方式进行布局。 这个项目的主要目标是研究这样的图 申述。特别是，我们建议研究丰富的联系 的结构、几何和拓扑属性之间 图形，并将它们应用于有关图形表示的基本问题(例如二维和三维图形绘制，以及图形在曲面上的嵌入)。将在研究中起关键作用的图的结构性质是从著名的罗伯逊和西摩的图子次理论中产生的那些性质。

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.