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.

摘要奖项：DMS-0636643 首席研究员：Alan W. Reid、Robert E. Gompf、Cameron M. Gordon、John E. Luecke 该 RTG 提案重点关注低维拓扑及其应用的培训。 低维流形的研究已成为数学研究活动的中心领域之一。 PI 在低维拓扑的几个不同领域拥有研究成果的既定记录；例如结理论、3 和 4 流形拓扑、双曲流形和辛拓扑。 该项目还将允许 PI 继续对博士后和学生进行培训。该 RTG 提案的主题与数学和应用科学的其他几个分支相互作用。 因此，它为各级研究、教育和培训经验提供了肥沃的土壤。该提案的主要特点之一是建立和提升数学系现有的成功的培训和教育结构。然而，我们提案的一个重要的新组成部分是跨学科研究培训。 这将为博士后、研究生和本科生提供不同于目前传统教育和培训的体验。 因此，我们的目标是提供一个框架，支持传统意义上的教育和培训，并为拓扑学在物理和生物科学中的应用提供培训经验的机会。作为后一项努力的一部分，该项目将促进与研究 DNA 和生物医学数学中打结现象的科学家的互动。 作为我们推广工作的一部分，我们将发起一系列公开讲座，以提高大学和当地社区对拓扑在其他科学中的作用的认识和认识水平。