Polar Varieties and Multiple Point Spaces

极坐标系和多点空间

• 批准号: EP/D040582/1
• 负责人: Kevin Houston
• 金额: $ 1.03万
• 依托单位: University of Leeds
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FD040582%2F1
• 关键词: Polar; Varieties; Multiple; Point; Spaces

This project concerns Singularity Theory - a branch of mathematics invented by Isaac Newton.In some sense the purpose of this research is simple. I wish to take a collection of objects and decide whether the objects are alike. An everyday example could be that the collection of objects is a group of school kids and I will say that the kids are alike if they are the same age.In a more mathematical setting I am interested in collections of curves, (but I can also work with really weird objects that live in higher dimensions). I want to take some measurements from each curve in the collection and from those measurements decide whether all the curves are alike. In other words I am looking for what are the important defining features.In the example of the group of school kids there is an obvious measurement to make: ask each one their age!I can take many measurements from my curves but what I really want is to make the smallest possible number of measurements for each curve. After all, there is no point in doing extra work!The techniques developed in this project can later be used in other subjects such as computer vision and robotics.

这个项目是关于奇点理论--牛顿发明的数学的一个分支。从某种意义上说，这个研究的目的很简单。我想收集一组物体，并判断这些物体是否相似。一个日常的例子可能是一组对象的集合是一群学校的孩子，我会说，如果他们是相同的年龄，孩子们是相似的。在一个更数学的设置，我感兴趣的曲线集合，（但我也可以与生活在更高维度的真正奇怪的对象）。我想对集合中的每条曲线进行一些测量，并根据这些测量来确定所有曲线是否都相似。换句话说，我在寻找什么是重要的定义特征。在学校孩子的例子中，有一个明显的测量：问每个人他们的年龄！我可以从我的曲线中进行许多测量，但我真正想要的是为每条曲线进行尽可能少的测量。毕竟，做额外的工作是没有意义的！在这个项目中开发的技术以后可以用于其他学科，如计算机视觉和机器人。