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

摘要奖：DMS-0602191主要研究者：Ralf Spatzier，Mario Bonk，Richard D. Canary，John E. Juha M. Fornaess海诺恩这项建议要求在密歇根大学的几何，拓扑和动力学的研究培训计划。 最近博士学位研究生和高级研究生将是主要受益者。数学系在UM有一个最大的和最有活力的博士后和研究生课程在全国与生产高qualityresearchers在几何，拓扑学和动力学的优秀记录。 该提案呼吁通过深化和扩大对所有这些领域的博士后和研究生的培训，并为他们提供充分的机会，使他们在研究中脱颖而出。 五名教师（马里奥邦克，理查德金丝雀，约翰埃里克Fornaess，尤哈海诺宁和拉尔夫Spatzier）将领导与其他11名高级教师合作这个项目。 该提案要求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讲习班，旅行学期，以加深在研究前沿的其他机构的科学培训，发展演讲技巧的机会，密集的指导和接触研究在这三个领域的本科生。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。 拓扑学研究的是在变形（如曲面上的孔洞）下保持不变的空间的性质。 动力学系统关注的是物理或数学系统随时间的演化，特别是近年来，它们在互利的相互作用中得到了发展。 低维的拓扑学、几何学和复杂动力学在许多方面都是相互联系的。 这些领域中许多最令人兴奋的发展是真正相互关联的，并且通过想法、类比或实际工具相互受益。 与此同时，与其他领域的联系，如代数几何和物理学也得到了极大的加强。 这些发展在广度和深度上都令人惊叹，并展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中培养研究人员，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.