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

摘要奖：DMS 0739208主要研究者：罗纳德A.放大图片作者：EfstratiaKalfagianni，托马斯H.放大图片作者：帕克沃尔夫森该提案的目标是在密歇根州立大学几何和拓扑学的研究培训环境的增强，建立在我们过去的成功。密歇根州立大学的几何/拓扑组长期致力于卓越的研究生和博士后培训：我们已经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）在所有层次的招聘-本科生，研究生和博士后。 （2）研究生培养，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和他们对终身职位的准备。 (4)本科生参与几何/拓扑研究小组。 （5）师生之间的互动。 (6)研究环境，在各级与定期计划的研讨会和访客。研究生和博士后助理谁将bementored根据这一建议将有助于研究几何和拓扑结构，使用各种各样的技术，包括规范理论，几何分析，pseudoholomorphicmaps，结不变量，手术技术，3流形拓扑结构，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在这些快速发展的领域取得了重要进展，预计未来的学生和博士后研究员将继续朝着这个方向发展。为了进一步刺激研究，MSU几何/拓扑组将为本科生、研究生和博士后研究员启动新的项目，并加强现有的项目。这些计划的关键是协同学习的氛围，已经由几何/拓扑组培育。这一建议将解决生产的研究数学家和数学教师谁感兴趣的几何学和拓扑学。该提案将支持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，他们正在由我们目前的RTG资助。 我们的目标是创造一个环境，让所有参与者成为更好的教师，更好的导师和更好的研究人员，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.