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

摘要奖：DMS-0353717主要研究人员：Ronald A.Fintushel，Efstra Kalfagianni，Thomas H.Parker，Jon G.Wolfson这项提议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。我们的目标是利用更多的资源来改进：1。各级招聘-本科生、研究生和博士后。研究生培训，特别是在研讨会、课程设置和缩短获得博士学位的时间方面。博士后研究员的经历以及他们为终身教职所做的准备。本科生参加几何/拓扑学研究小组。各级师生之间的互动。所有级别的研究环境都有定期的研讨会和访问数学家。根据这项建议，研究生和博士后助理将使用广泛的技术，包括规范理论、几何分析、伪全纯映射、纽结不变量、外科技术和映射班组，为我们的主要重点--低维流形--的研究做出贡献。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个快速发展的领域中取得了重要进展，预计未来的学生和博士后研究员将继续朝着这个方向前进。为了进一步刺激研究，密歇根州立大学几何/拓扑学小组将为本科生和研究生以及博士后研究员发起新的项目。这些研讨会的关键是过去15年来几何/拓扑学小组所营造的协作学习氛围。这项提议的更广泛影响将涉及对几何和拓扑学感兴趣的研究数学家和数学教师的成果。其目的是创造一种环境，鼓励所有参与者成为更好的教师、更好的说明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。

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.