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：DMS-0636643主要研究者：Alan W.作者声明：Robert E. Gompf，卡梅隆M.作者：John E. LueckeRTG的建议主要集中在低维拓扑及其应用的训练上。 低维流形的研究已成为数学研究的中心领域之一。 PI在低维拓扑学的几个不同领域都有研究成果，例如纽结理论，3和4流形拓扑，双曲流形和辛拓扑。 该项目还将允许PI继续他们对博士后和学生的培训。这个RTGProposal的主题与数学的其他几个分支以及应用科学相互作用。 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改进数学系目前成功的培训和教育结构。然而，我们建议的一个重要的新组成部分是跨学科研究的培训。 这将为博士后、研究生和本科生提供不同于目前传统的教育和培训经验。 因此，我们的目标是提供一个框架，支持传统意义上的教学教育和培训，并提供机会，在物理和生物科学中的应用拓扑学的培训经验。作为后者努力的一部分，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，我们将发起一个公开讲座系列，这将提高在大学和当地社区的其他科学拓扑学的作用的形象和意识水平。