Research Training in Geometry at the Interface with Physics

几何与物理交叉的研究培训

• 批准号: 0502267
• 负责人: H. Blaine Lawson
• 金额: --
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0502267&HistoricalAwards=false
• 关键词: Research; Training; Geometry; Interface; Physics

This is a proposal to harness the special resources at StonyBrook to train students and post-docs in geometry and itsinteraction with mathematical physics. The plan involves aradical shift from standard curricula and should be broadlyappealing to young people who are considering the possibility of acareer in mathematics.Stony Brook has a large, highly active (and interactive) groupof geometers representing nearly all aspects of the fieldfrom algebraic geometry to string topology.A substantial part of the research of this group is related to and/orinspired by modern physics, and there is a long tradition ofinteraction between Stony Brook's mathematicians and physicists. This isrepresented in collaborations, seminars, joint students, andconferences, as well as two major programs in mathematics andphysics, funded outside the NSF. This is a proposal to use theseresources in new, effective ways for the training of young researchers.The proposal aims at: (1) incorporating the high-level seminars andworkshops into the training of students at an early point by closementoring, (2) bringing students more quickly and effectively to theresearch level, (3) training students and post-docs in the dual culturesof geometry and physics, (4) giving undergraduates a taste ofmathematical research at the interactive level.If successful this could lead to an adoption of new models forundergraduate development and graduate education. It should producemore effective researchers and therefore lead to better careersin mathematics. A fundamental outcome would be the attraction of moreU.S. citizens into mathematics in general and these fields inparticular, because this program offers close personal supervision, an interactive and challenging environment and strong intellectualappeal. Another important outcome would be a new generation trainedfrom the beginning in the dual cultures of mathematics and physics.This should lead to even greater communication between these fields inthe future.

这是一项利用石溪分校特殊资源来培训学生和博士后几何及其与数学物理相互作用的建议。该计划涉及到从标准课程的根本转变，应该广泛吸引那些正在考虑在数学方面从事职业的年轻人。（和交互式的）几何学家的团体，代表了从代数几何到弦拓扑学的几乎所有领域。这个团体的研究的很大一部分与现代物理学有关或受其启发，斯托尼布鲁克的数学家和物理学家之间有着悠久的互动传统。这体现在合作，研讨会，联合学生，和会议，以及数学和物理学的两个主要项目，由国家科学基金会资助。 这是一项以新的、有效的方式利用这些资源培训青年研究人员的建议，其目的是：（1）通过密切的指导，在早期将高水平的研讨会和讲习班纳入学生的培训中，（2）使学生更快、更有效地达到研究水平，（3）在几何和物理的双重文化中培训学生和博士后，（4）让本科生在互动的层次上体验数学研究，如果成功的话，这可能会导致本科生发展和研究生教育采用新的模式。 它应该产生更有效的研究人员，因此导致更好的职业生涯在数学。一个根本的结果将是吸引更多的美国人。公民进入数学一般和这些领域，特别是因为这个计划提供了密切的个人监督，互动和具有挑战性的环境 and strong强大intellectual智力appeal上诉. 另一个重要的结果是新一代人从一开始就在数学和物理的双重文化中接受训练。这将在未来导致这两个领域之间更大的交流。