The Structure and Geometry of Graphs

图是无处不在的数学结构，它对信息流、运输网络和生化途径等关系信息进行建模。通常希望有一个图形的几何表示法。例如，如果程序中的信息流由视觉上吸引人的图画来表示，程序员将更好地理解计算机程序。该项目的重点将是图结构理论和图的几何性质之间的相互作用。此外，该项目将在数学和计算机科学的其他领域有重要的应用，包括计算复杂性、数据结构分析和三维信息可视化。

Graphs are ubiquitous mathematical structures that model relational information such as information flows, transportation networks, and biochemical pathways. It is often desirable to have a geometric representation of a graph. For example, a programmer will better understand a computer program if the flow of information within the program is represented by a visually appealing drawing. The focus of the project will be the interplay between graph structure theory and geometric properties of graphs. Moreover, the project will have significant applications to other area of mathematics and computer science, including computational complexity, analysis of data structures, and three-dimensional information visualisation.