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: 0739208
• 负责人: Ronald Fintushel
• 金额: $ 58.39万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0739208&HistoricalAwards=false
• 关键词: EMSW21; RTG; Research; Training; Geometry

AbstractAward: DMS 0739208Principal Investigator: Ronald A. Fintushel, EfstratiaKalfagianni, Thomas H. Parker, Jon G. WolfsonThe goal of this proposal is the enhancement of the researchtraining environment in geometry and topology at Michigan StateUniversity, building on our past success. The Geometry/TopologyGroup at MSU has a long-standing commitment to excellence ingraduate and postdoctoral training: we have produced someoutstanding graduate students, and we have been fortunate to haverecruited and mentored exceptional postdoctoral fellows. Ourgoal is to use increased resources to improve: (1) Recruitment atall levels --- undergraduate, graduate, and postdoctoral. (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 theirpreparation for a tenure-track position. (4) Undergraduateparticipation with the Geometry/Topology research group. (5)Interaction among students and faculty at all levels. (6) Theresearch environment at all levels with a regular program ofseminars and visitors.The graduate students and postdoctoral assistants who will bementored under this proposal will contribute to research ingeometry and topology, using a wide variety of techniquesincluding gauge theory, geometric analysis, pseudoholomorphicmaps, knot invariants, surgery techniques, 3-manifold topology,and mapping class groups. Faculty at Michigan State Universityas well as former students and postdoctoral assistants have takenpart in important advances in these rapidly progressing areas,and it is expected that future students and postdoctoral fellowswill continue in this direction. To further stimulate research,the MSU Geometry/Topology Group will initiate new programs andenhance existing programs for undergraduate and graduate studentsand postdoctoral fellows. The key to these programs is theatmosphere of collaborative learning that has been fostered bythe Geometry/Topology Group.This proposal will address the production of researchmathematicians and teachers of mathematics who are interested ingeometry and topology. This proposal will support 5 new graduatestudents and 2 new postdoctoral associates as well as one postdocand one graduate student who are being supported by our currentRTG grant. Our aim is to create an environment which encouragesall involved to become better teachers, better expositors, andbetter researchers, and encourages those entering mathematics tostay in the field.

摘要：项目负责人：Ronald A. Fintushel, EfstratiaKalfagianni, Thomas H. Parker, Jon G. wolfson本提案的目标是在我们过去成功的基础上，加强密歇根州立大学几何和拓扑的研究培训环境。密歇根州立大学的几何/拓扑小组长期致力于优秀的研究生和博士后培训：我们培养了一些优秀的研究生，我们很幸运地招募和指导了杰出的博士后研究员。我们的目标是利用增加的资源来改善：(1)各级招聘——本科生、研究生和博士后。(2)研究生培训，特别是在研讨会、课程设置的多样性和缩短获得博士学位的时间方面。(3)博士后的经历及其为获得终身职位所做的准备。(4)本科生参与几何/拓扑研究小组。(5)各级师生之间的互动。(6)各级的研究环境，定期安排研讨会和访问。在本计划指导下的研究生和博士后助理将对几何几何学和拓扑学的研究做出贡献，使用各种各样的技术，包括规范理论、几何分析、伪全纯映射、结不变量、手术技术、3流形拓扑和映射类群。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参与了这些快速发展领域的重要进展，预计未来的学生和博士后研究员将继续朝这个方向发展。为了进一步促进研究，密歇根州立大学几何/拓扑小组将启动新的项目，并加强现有的本科生、研究生和博士后项目。这些课程的关键是由几何/拓扑小组培养的协作学习氛围。本提案将解决对几何和拓扑学感兴趣的研究数学家和数学教师的生产。本提案将支持5名新的研究生和2名新的博士后助理，以及一名博士后和一名研究生，他们正在获得我们当前trtg资助。我们的目标是创造一种环境，鼓励所有参与者成为更好的教师，更好的讲解者和更好的研究人员，并鼓励那些进入数学领域的人留在这个领域。