EMSW21-RTG: Training the Research Workforce in Geometry, Topology and Dynamics

摘要奖：DMS-0602191首席研究员：Ralf Spatzier，Mario Bonk，Richard D.Canary，John E.ForNaess，Juha M.Heinonen这项提案要求在密歇根大学开展几何、拓扑和动力学方面的研究培训计划。S博士和高级研究生将是主要受益者。密歇根大学数学系拥有美国规模最大、最具活力的博士后和研究生项目之一，在培养几何、拓扑和动力学方面的高素质研究人员方面有着出色的记录。这项提议呼吁通过深化和扩大所有这些领域的博士后和研究生培训，并为他们提供充分的机会在他们的研究中脱颖而出，来支持他们的培训。五名教员(Mario Bonk、Richard Canary、JohnErik ForNaess、Juha Heinonen和Ralf Spatzier)将与其他11名资深教员一起领导这个项目。该提案呼吁在培训计划中进行几项具体的创新：提供密集的探索性研讨会和研讨会、旅行学期以深化在其他研究前沿场所的科学培训、发展授课技能的机会、向本科生集中指导和接触这三个领域的研究。几何、拓扑和动力系统是数学的核心领域。几何学通过曲率等不变量来研究空间的形状。拓扑学研究在变形下保持不变的空间的性质，例如曲面上的孔洞的数量。动力系统研究的是一个物理或数学系统随时间的演变。特别是在最近几年，它们在互惠互利的互动中发展起来。低维的拓扑学、几何学和复杂动力学就是一个很好的例子，它们在许多方面都是相互映照的。这些领域中许多最令人兴奋的发展是真正相互关联的，并从彼此的想法、类比或实际工具中受益。与此同时，与代数几何和数学物理等其他领域的联系也显著加强。这些发展在广度和深度上都令人惊叹，显示了这些领域的活力。该项目将在这些令人兴奋和相互关联的领域培训年轻研究人员，并将有助于确保他们未来的健康和持续的互动。

AbstractAward: DMS-0602191Principal Investigator: Ralf Spatzier, Mario Bonk, Richard D. Canary, John E. Fornaess, Juha M. HeinonenThis proposal calls for a research training program in geometry,topology and dynamics at the University of Michigan. RecentPh.D.'s and advanced graduate students will be the mainbeneficiaries. The Mathematics Department at UM has one of thelargest and most vigorous post-doctoral and graduate programs inthe country with an excellent record of producing high-qualityresearchers in geometry, topology and dynamics. This proposalcalls to bolster the training of post-docs and graduate studentsin all of these areas by deepening and broadening it andproviding them with ample opportunities to excel in theirresearch. Five faculty members (Mario Bonk, Richard Canary, JohnErik Fornaess, Juha Heinonen and Ralf Spatzier) will lead thisproject in collaboration with eleven other senior faculty. Theproposal calls for several specific innovations in the trainingprogram by: providing intensive exploratory seminars andworkshops, travel semesters to deepen the scientific training atother insitutions at the forefront of research, opportunities todevelop lecturing skills, intensive mentoring and exposure toresearch in the three areas to undergraduates.Geometry, topology and dynamical systems are core areas ofmathematics. Geometry investigates the shape of spaces, throughinvariants such as curvature. Topology explores the propertiesof spaces which remain invariant under deformations such as thenumber of holes in a surface. Dynamical systems concern theevolution of a physical or mathematical system over time.Especially in recent years, they have developed in mutuallybeneficial interaction. Case in point are topology, geometry andcomplex dynamics in low dimension which in many aspects mirroreach other. Many of the most exciting developments in theseareas are truly interrelated, and benefit from each other eitherby idea, analogy or actual tool. At the same time, connectionswith other fields such as algebraic geometry and mathematicalphysics have strengthened dramatically. These developments havebeen amazing in their breadth and depth, and demonstrate thevitality of these areas. This project will train youngresearchers in these exciting and interconnected fields, and willhelp insure their future health and continued interaction.