Research Training in Geometry at the Interface with Physics

这是一项利用石溪的特殊资源来培养学生和博士后几何学及其与数学物理的相互作用的建议。该计划涉及对标准课程的彻底转变，应该会对那些考虑从事数学职业的年轻人产生广泛的吸引力。Stony Brook拥有一个庞大的、高度活跃的（和互动的）几何学者群体，他们代表了该领域从代数几何到弦拓扑的几乎所有方面。这个小组的大部分研究都与现代物理学有关或受到现代物理学的启发，并且在石溪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，以及两个主要的数学和物理项目中，这些项目都是由国家科学基金会资助的。这是一个以新的、有效的方式利用这些资源来培训年轻研究人员的建议。该提案旨在：(1)通过密切监督，将高水平的研讨会和讲习班纳入学生的早期培训中；(2)使学生更快、更有效地进入研究水平；(3)培养学生和博士后在几何和物理的双重文化中；(4)让本科生在互动层面上体验数学研究。如果成功，这可能会导致本科发展和研究生教育采用新的模式。它应该培养出更高效的研究人员，从而导致更好的数学事业。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，特别是这些领域，因为这个程序提供了密切的个人监督，一个互动和具有挑战性的环境和强大的智力吸引力。另一个重要的结果是新一代从一开始就接受数学和物理双重文化的训练。这将导致未来这些领域之间更大的交流。

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.