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

EMSW21-RTG：几何、拓扑和动力学方面的研究人员培训

• 批准号: 0602191
• 负责人: Ralf Spatzier
• 金额: $ 249.92万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-01 至 2012-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0602191&HistoricalAwards=false
• 关键词: EMSW21; RTG; Training; Research; Workforce

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.

Abstractaward：DMS-0602191原理研究员：Ralf Spatzier，Mario Bonk，Richard D. Canary，John E. Forneess，Juha M. Heinonenthis提案要求密歇根大学的几何学，拓扑，拓扑，拓扑和动力学进行研究培训计划。 近期的Ph.D。和高级研究生将成为主题。 UM的数学部门是该国最大，最有活力的博士后和研究生课程之一，在几何，拓扑和动态方面生产高质量的研究者。 通过加深和拓宽并为他们提供了足够的机会，可以在所有这些领域中加强所有这些领域的培训，以加强对所有这些领域的培训。 五名教职员工（Mario Bonk，Richard Canary，Johnerik Forneess，Juha Heinonen和Ralf Spatzier）将与其他11位高级教师合作。 Proposal要求在培训计划中进行几项特定的创新，作者：提供密集的探索性研讨会和工作室，旅行学期，以加深研究的科学培训，在研究的最前沿，机遇的机会，培训技能的机会，密集的指导和曝光，拓扑和动态系统是数学的核心领域。几何形状研究了空间的形状，包括曲率等广发生器。 拓扑探讨了在变形下保持不变的空间的特性，例如表面孔的孔。 动力系统涉及随着时间的推移的物理或数学系统的发展。尤其是近年来，它们在互惠互动中发展。 在低维中的拓扑，几何形状和复杂动力学中，这在许多方面都反映了其他方面。 Theeareas中许多最令人兴奋的发展都是真正相互关联的，并且可以通过想法，类比或实际工具彼此受益。 同时，与代数几何和数学物理等其他领域的连接急剧增强。 这些发展使它们的广度和深度令人惊奇，并展示了这些领域的景象。 该项目将在这些令人兴奋和相互联系的领域中培训Youngresearchers，Willhelp确保他们的未来健康并继续互动。