Distributed obstruction finding and fullerene research

所要求的设备包括工作站的研究生和本科生，这将是在我们的理论实验室和一些处理器无显示器，使广泛的分布式计算两个研究问题。在图论中最著名的定理之一是库拉托夫斯基定理：如果一个图不能画在一个平面上没有交叉线，那么它必须包含一个子图同胚的两个图之一。我的研究计划的一个主要目标是为环面（形状像甜甜圈的表面）找到一个类似的定理。额外的计算资源将极大地促进对这些障碍物的搜索，以及找到计算机辅助证明我们所发现的障碍物集是完整的最终目标。有一个完整的障碍集可以用来证明定理的环形图，并会给洞察力，如何设计简单，快速算法绘制他们的图片。富勒烯是全碳分子，其结构是3-正则平面图的面大小为5或6。我们已经开发了一个程序，FuiGui来帮助这些分子及其参数的可视化。我们的目标是积累一个大型数据库的参数信息的所有小富勒烯，以调查这些参数和重要的化学性质的富勒烯之间的相关性。额外的计算设施对于在合理的时间内收集这些数据至关重要。

The equipment requested includes workstations for graduate and undergraduate students which will be publically available in our theory lab and some processors without monitors to enable extensive distributed computations for two research problems.One of the most famous theorem in graph theory is Kuratowski's theorem: if a graph cannot be drawn on a plane with no crossing lines then it must contain a subgraph homeomorphic to one of two graphs. One major ongoing goal of my research program is to find a similar theorem for a torus (a surface shaped like a doughnut). Extra computational resources would greatly facilitate searching for these and the ultimate goal of finding a computer-aided proof that the set of obstructions we have found is complete. Having a complete set of obstructions could be used to prove theorems about toroidal graphs and would give insight as to how to design simple, fast algorithms for drawing pictures of them.Fullerenes are all-carbon molecules whose structures are 3-regular planar graphs with face sizes five or six. We have developed a program, FuiGui to aid in the visualization of these molecules and their parameters. Our goal is to amass a large database of parameter information for all the small fullerenes in order to investigate correlations between these parameters and important chemical properties of fullerenes. Extra computational facilities are critical for collecting this data in a reasonable amount of time.