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学和拓扑学领域的教育，为他们提供互动论坛，以扩大他们的知识，并通过财政支助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学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、辛几何和拓扑学、低维拓扑和双曲几何、几何和代数拓扑以及代数几何。 除了所涵盖的领域的广度，斯坦福大学的几何和拓扑研究小组是由重叠的利益和活动的网络连接。 这个项目的目的是吸引学生加入这个群体，让他们更充分地受益于它所代表的广泛的专业知识。为了促进学生和教师之间的互动，代表这些不同的利益，具体的研讨会计划。 这些将由资深教师管理，并将涉及研究生，博士后研究人员，并在某些情况下，先进的本科生，谁是在这些领域感兴趣。 这样的研讨会的例子包括以下：1）经典研讨会：学生将提出，在教员的监督下，各种"经典论文”，改变了他们各自的领域的数学。2）进展研讨会：更先进的研究生和博士后研究人员将详细讨论他们的工作，因为他们正在努力。3）数学家物理研讨会：几何/拓扑学学生将在数学和物理教师的共同监督下学习物理学的相关领域。该提案旨在为斯坦福大学数学研究生课程带来更多的美国公民/永久居民。 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增加斯坦福大学本科生的规模，提高他们在美国大学攻读研究生课程的质量;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.