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

项目负责人：Ronald A. Fintushel, Efstratia Kalfagianni,Thomas H. Parker, Jon G. wolfson，目的是改善密歇根州立大学几何和拓扑的研究培训环境。我们的目标是利用增加的资源来改进：各层次招聘——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，以及缩短获得ap . d .3的时间。博士后的经历和他们为获得终身职位所做的准备。4 .本科生参加几何/拓扑研究小组。学生和教师之间的互动，各级。在各个层次的研究环境中，定期举办研讨会和访问数学家。在本计划指导下的研究生和博士后助理将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、手术技术和映射类群，对我们的主要重点低维流形进行研究。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一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。为了进一步刺激研究，密歇根州立大学几何/拓扑小组将为本科生、研究生和博士后启动新的项目。这些研讨会的关键是协作学习的氛围，这是由几何/拓扑小组在过去的15年中所培养的。该提案的广泛影响将解决对几何和拓扑感兴趣的研究数学家和数学教师的生产。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。

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.