Conference on Topology and Geometry in Dimension Three: Triangulations, Invariants, and Geometric Structures; June 2010; Oklahoma City, OK

第三维度拓扑和几何会议：三角剖分、不变量和几何结构；

基本信息

批准号：
1005383
负责人：
Weiping Li
金额：
$ 2.28万
依托单位：
Oklahoma State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2010
资助国家：
美国
起止时间：
2010-05-01 至 2011-04-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1005383&HistoricalAwards=false
关键词：
Conference Topology Geometry Dimension Three

项目摘要

The Conference on "Topology and Geometry in Dimension Three: Triangulations, Invariants, and Geometric Structures" will be held at Oklahoma State University, June 4-6, 2010. The conference brings together experts and emerging researchers to report on recent results and explore future directions in the study and understanding of 3-manifolds. Geometric structures on 3-manifolds are known to exist but relatively little is known about direct construction of these geometric structures; specifically, constructing the geometry from a description, such as a Heegaard splitting or triangulation of the manifold. This conference will highlight finding direct connections between topological structures on 3-manifolds (triangulations in particular) and geometric structures and expanding the use of these structures to a study of new invariants and applications of hyperbolic geometry to 3-manifolds.Three-dimensional space provides the local space-model for much of science and engineering. Three-manifolds are locally modeled on three-dimensional space and their study and understanding leads to better predictions and understanding in science and more effective applications in engineering and technology. Recent advances in our understanding of three-manifolds has generated new energy making it one of the most exciting and rapidly advancing areas in mathematics; and making this Conference very timely for reporting on emerging results and plotting future directions.

“第三维拓扑和几何：三角剖分、不变量和几何结构”会议将于 2010 年 6 月 4 日至 6 日在俄克拉荷马州立大学举行。会议汇集了专家和新兴研究人员，报告最新成果并探讨未来3-流形的研究和理解的方向。已知存在 3 流形上的几何结构，但对这些几何结构的直接构造知之甚少；具体来说，根据描述构造几何形状，例如流形的 Heegaard 分裂或三角剖分。本次会议将强调寻找3-流形上的拓扑结构（特别是三角剖分）与几何结构之间的直接联系，并将这些结构的使用扩展到新的不变量的研究以及双曲几何在3-流形上的应用。三维空间提供了大多数科学和工程的局部空间模型。三流形是在三维空间上进行局部建模的，它们的研究和理解可以带来更好的科学预测和理解以及工程和技术中更有效的应用。我们对三流形理解的最新进展产生了新的能量，使其成为数学中最令人兴奋和发展最快的领域之一；并使本次会议非常及时地报告新出现的成果并规划未来的方向。