EMSW21-RTG-Program in low-dimensional topology and its applications

低维拓扑中的EMSW21-RTG-程序及其应用

• 批准号: 0636643
• 负责人: Alan Reid
• 金额: $ 124.99万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-06-01 至 2013-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0636643&HistoricalAwards=false
• 关键词: EMSW21; RTG; Program; low; dimensional

AbstractAward: DMS-0636643Principal Investigator: Alan W. Reid, Robert E. Gompf,Cameron M. Gordon, John E. LueckeThis RTG proposal is focused on training in low-dimensionaltopology and its applications. The study of low-dimensionalmanifolds has become one of the central areas of researchactivity in mathematics. The PI's have an establishedtrack-record of research accomplishments in several differentareas of low-dimensional topology; for example knot theory, 3 and4-manifold topology, hyperbolic manifolds and symplectictopology. The project will also allow the PI's to continue theirtraining of postdocs and students. The subject of this RTGProposal interacts with several other branches of mathematics aswell as the applied sciences. It therefore provides fertileground for research, education and training experiences at alllevels.One of the main features of the proposal is to build, andelevate, the successful structure for training and educationcurrently in place in the Department of Mathematics. However, animportant new component of our proposal is training forinterdisciplinary research. This will afford postdocs, graduateand undergraduate students educational and training experiencesdifferent from the traditional ones available at present. Wetherefore aim to provide a framework that supports education andtraining by instruction in the traditional sense, and alsoprovide opportunity for training experiences in applications oftopology in the physical and biological sciences. As part of thislatter effort the project will promote interactions withscientists studying knotting phenomena in DNA and biomedicalmathematics. As part of our outreach efforts, we will instigatea public lecture series that will raise the profile and level ofawareness of the role of topology in other sciences in theUniversity and local community.

Abstractaward：DMS-0636643原理研究者：Alan W. Reid，Robert E. Gompf，Cameron M. Gordon，John E. Lueckethis RTG提案专注于低维度学及其应用中的培训。 对低维曼群的研究已成为数学研究效率的中心领域之一。 PI在低维拓扑的几个不同方案中拥有既定的研究成就；例如结理论，3和4个manifold拓扑，双曲线歧管和符号学。 该项目还将允许PI继续对博士后和学生进行培训。该RTGProposal的主题与应用科学的其他几个数学分支相互作用。 因此，它为Alllevel的研究，教育和培训经验提供了肥沃的地面。该提案的主要特征之一是在数学系建立，Andelevate，这是成功培训和教育的成功结构。但是，我们提案的动画新组成部分是培训Interdogedrinary Research的培训。 这将提供博士后，毕业的本科生教育和培训经验与目前可用的传统经验不同。 因此，旨在提供一个框架，以传统意义上的教学来支持教育和训练，以及在物理和生物科学中培训应用体验中培训经验的机会。作为此措施的一部分，该项目将促进与研究DNA和生物医学仪器中研究打结现象的互动。 作为我们推广工作的一部分，我们将启动公开讲座系列，这些系列将提高拓扑在大学和本地社区其他科学中作用的概况和水平。