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

摘要奖：DMS 0739208首席研究员：Ronald A.Fintushel，EfstraKalfagianni，Thomas H.Parker，Jon G.Wolfson这项提议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学的研究培训环境。密歇根州立大学几何/拓扑学小组长期致力于卓越的教育和博士后培训：我们培养出了一些优秀的研究生，我们幸运地拥有了优秀的博士后研究员。我们的目标是利用更多的资源来改进：(1)在所有级别-本科生、研究生和博士后--招聘。(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)博士后研究员的经验及其为终身教职职位做准备。(4)本科生参加几何/拓扑学研究组。(5)各级师生之间的互动。(6)各级研究环境，定期安排研讨会和访问者。根据这一建议，研究生和博士后助理将使用各种技术，包括规范理论、几何分析、伪全纯映射、纽结不变量、外科技术、三维流形拓扑学和映射类群，为几何和拓扑学的研究做出贡献。密歇根州立大学的教师以及以前的学生和博士后助理在这些快速进步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/拓扑学小组将启动新的计划，并加强现有的本科生、研究生和博士后研究员计划。这些计划的关键是几何/拓扑学小组营造的协作学习氛围。这项建议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成果。这项提议将支持5名新的毕业生和2名新的博士后助理，以及1名博士后和1名研究生，他们正在得到我们目前的RTG赠款的支持。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 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.