EMSW21-RTG Research Training in Geometry and Topology at Michigan State University

密歇根州立大学几何和拓扑学 EMSW21-RTG 研究培训

• 批准号: 0353717
• 负责人: Ronald Fintushel
• 金额: --
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-15 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0353717&HistoricalAwards=false
• 关键词: EMSW21; RTG; Research; Training; Geometry

AbstractAward: DMS-0353717Principal Investigators: Ronald A. Fintushel, Efstratia Kalfagianni,Thomas H. Parker, Jon G. wolfsonThe goal of this proposal is the enhancement of the researchtraining environment in geometry and topology at Michigan StateUniversity. Our goal is to use increased resources to improve:1. Recruitment at all levels --- undergraduate, graduate, andpostdoctoral.2. Graduate training, especially in terms of the diversity ofseminars, course offerings, and reducing the time to obtain aPh.D.3. The experience of postdoctoral fellows and their preparationfor a tenure-track position.4. Undergraduate participation with the Geometry/Topologyresearch group.5. Interaction among students and faculty at all levels.6. The research environment at all levels with a regular programof seminars and visiting mathematicians.The graduate students and postdoctoral assistants who will bementored under this proposal will contribute to research on ourmain focus, low-dimensional manifolds, using a wide variety oftechniques including gauge theory, geometric analysis,pseudoholomorphic maps, knot invariants, surgery techniques, andmapping class groups. Faculty at Michigan State University aswell as former students and postdoctoral assistants have takenpart in important advances in this rapidly progressing area, andit is expected that future students and postdoctoral fellows willcontinue in this direction.To further stimulate research, the MSU Geometry/Topology Groupwill initiate new programs for undergraduate and graduatestudents and postdoctoral fellows. The key to these seminars isthe atmosphere of collaborative learning that has been fosteredby the Geometry/Topology Group over the last fifteen years. Thebroader impact of this proposal will address the production ofresearch mathematicians and teachers of mathematics who areinterested in geometry and topology. The aim is to create anenvironment which encourages all involved to become betterteachers, better expositors, and better researchers, andencourages those entering mathematics to stay in the field.

摘要奖：DMS-0353717主要研究者：罗纳德A.放大图片作者：Efstratia Kalfagianni，托马斯H.放大图片作者：帕克该提案的目标是加强密歇根州立大学几何和拓扑学的研究培训环境。 我们的目标是利用增加的资源来改善：1。招收本科生、研究生、博士后.研究生培训，特别是在研讨会，课程设置的多样性方面，并减少获得博士学位的时间。博士后研究员的经验和他们对终身职位的追求.本科生参与几何/拓扑研究小组。各级师生互动。在各级的研究环境与定期计划的研讨会和访问数学家。研究生和博士后助理谁将bementrained根据这一建议将有助于研究我们的主要重点，低维流形，使用各种各样的技术，包括规范理论，几何分析，pseudoholomorphic映射，结不变量，手术技术，和映射类组。 密歇根州立大学的教师以及以前的学生和博士后助理已经在这一快速发展的领域取得了重要进展的一部分，并预计未来的学生和博士后研究员将继续在这一方向。为了进一步刺激研究，密歇根州立大学几何/拓扑组将启动新的本科生和研究生和博士后研究员计划。这些研讨会的关键是协作学习的氛围，这是由几何/拓扑组在过去的十五年里培养的。更广泛的影响，这一建议将解决生产的研究数学家和数学教师谁是感兴趣的几何和拓扑结构。其目的是创造一个环境，鼓励所有参与成为更好的教师，更好的导师，更好的研究人员，并鼓励那些进入数学留在外地。