Research Training in Geometry at the Interface with Physics

这是一项利用斯坦布鲁克的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。这项计划涉及从标准课程到普通课程的转变，应该会广泛地吸引那些正在考虑从事数学职业的年轻人。斯通布鲁克有一个庞大的、高度活跃(和互动)的几何学家小组，他们几乎代表了该领域的各个方面，从代数几何到弦拓扑学。这个小组的大部分研究都与现代物理学有关和/或受到其启发，石溪的数学家和物理学家之间的互动有着悠久的传统。这体现在合作、研讨会、联合学生和会议，以及NSF以外资助的两个主要的数学和物理项目上。这是一项以新的、有效的方式利用资源培训年轻研究人员的建议。该建议旨在：(1)通过结束教学，将高级别研讨会和工作坊纳入学生的早期培训，(2)更快、更有效地将学生带到研究水平，(3)在几何和物理双重文化中培训学生和博士后，(4)让本科生在互动层面上体验数学研究。如果成功，可能会导致采用新的本科生发展和研究生教育模式。它应该产生更多有效的研究人员，从而在数学上带来更好的职业生涯。一个根本的结果将是吸引更多的美国公民进入数学领域，特别是这些领域，因为这个项目提供了密切的个人监督、互动和具有挑战性的环境以及强大的智力吸引力。另一个重要的结果是，从一开始就在数学和物理双重文化中培养的新一代。这应该会在未来导致这些领域之间更好的交流。

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.