EMSW21-RTG: Training Students in Geometry and Topology at Stanford University

该项目的目标是加强斯坦福大学学生在几何和拓扑学领域的教育，为他们提供互动论坛，以拓宽他们的知识，并通过财政支持为他们提供参加这些论坛的时间。斯坦福大学在几何和拓扑方面有一个广泛而活跃的研究小组，研究人员包括几何分析、微分几何和极小曲面、辛几何和拓扑、低维拓扑和双曲几何、几何和代数拓扑以及代数几何。除了所涉及领域的广度之外，斯坦福大学几何和拓扑学研究小组还通过一个重叠的兴趣和活动网络联系在一起。这个项目的目的是吸引学生加入这个群体，并让他们更充分地受益于它所代表的广泛专业知识。为了促进代表这些不同兴趣的学生和教职员工之间的互动，我们计划了具体的研讨会。这些课程将由资深教职员工管理，将涉及研究生、博士后研究人员，在某些情况下，还包括对这些领域感兴趣的高级本科生。这类研讨会的例子包括：1)经典研讨会：学生将在一名教师的指导下提交各种改变各自数学领域的“经典论文”。2)进步研讨会：更高级的研究生和博士后研究人员将详细讨论他们正在进行的工作。3)数学家的物理研讨会：几何/拓扑学的学生将在数学和物理学院的联合指导下学习相关的物理领域。该提议旨在吸引更多的美国公民/永久居民参加斯坦福大学的数学研究生项目。将特别注意吸引更多的妇女和少数民族参加该方案。这里提出的活动还应该扩大斯坦福大学在美国大学攻读研究生课程的本科生的规模和质量；这些学生中的大多数是美国公民或永久居民。

The goal of this project is to enhance the education of students in the areas of geometry and topology at Stanford by providing them with interactive forums in which to broaden their knowledge and by providing them with the time, through financial support, to participate in those forums. Stanford has a broad and active research group in geometry and topology with researchers in geometric analysis, differential geometry and minimal surfaces, symplectic geometry and topology, low-dimensional topology and hyperbolic geometry, geometric and algebraic topology, and algebraic geometry. Aside from the breadth of fields covered, the Stanford research group in geometry and topology is connected by a network of overlapping interests and activities. The purpose of this project is to attract students into this group and to allow them to more fully benefit from the broad expertise it represents. In order to facilitate the interaction between students and faculty representing these varied interests, specific seminars are planned. These will be run by senior faculty members and will involve graduate students, postdoctoral researchers, and, in some cases, advanced undergraduates, who are interested in these fields. Examples of such seminars include the following:1) Classics seminar: Students will present, under the supervision of a faculty member, various ``classical papers" that transformed their respective areas of mathematics.2) Progress seminar: More advanced graduate students and postdoctoral researchers will discuss their work in detail, as they are working on it.3) Physics for mathematicians seminar: Geometry/topology students will study a relevant area of Physics under the joint supervision of the Mathematics and Physics faculty.The proposal is designed to bring more US citizens/permanent residents to the Stanford graduate program in mathematics. Special attention will be given to attracting more women and minorities to the program. The activities proposed here should also increase the size and improve the quality of the pool of Stanford undergraduates who go to graduate programs at US universities; the majority of these students are US citizens or permanent residents.