Mathematical Sciences: Small Geometry Project

本科生课题研究经验 12名学生将获得该奖项。 学生将 在七名教师的监督下工作十周 顾问。 其他资金将支持更多的 学生使该团体的总人数达到约20人。 的 拨款更新对类似规模的成功项目的资助 在过去三年中进行的。 尽管许多 参与者尚未毕业，至少有七人已知 攻读数学和计算机研究生 科学 该计划的结构，使每个学生的工作与 两个小组。 他们最初专注于几个问题， 其中一个是最有希望的 主题是几何的 尽管标题中的术语“小”是代表 第一组顾问的首字母缩写，不用作 形容词 典型的问题领域将包括 涉及纽结理论 学生将考虑如何分析 结的交叉可以提供关于它们的 一般分类 这些想法与其他想法有关， 图论中的某些节点可以嵌入图中。 人们想刻画这样的图。 其他主题包括 拓扑特征的计算称为Betti 数字，向量值厄米特形式产生的 微分几何的柯西-黎曼结构和工作 算术除数问题的解析数论 进步。 学生将从新英格兰地区招募。 将努力确保研究在结束后继续进行。 夏天结束了。 这将是特别真实的学生， 都是从威廉姆斯学院招募的 据估计， 该项目将产生一些可编辑的文件， 学生将有机会展示他们的工作， 专业会议。

A Research Experiences for Undergraduates project involving 12 students will be supported by this award. The students will work for ten weeks under the supervision of seven faculty advisors. Other funds will provide support for additional students bringing the total size of the group to about 20. The grant renews funding of successful projects of similar size carried out during the past three years. Although many of the participants have not yet graduated, at least seven are known to be enrolled in graduate study in mathematics and computer science. The program is structured so that each student works with two subgroups. They focus on several problems initially until one emerges as the most promising. The themes are geometric although the term SMALL in the title is an acronym representing the initials of the first group of advisors and is not used as an adjective. Typical problems areas will include questions involving knot theory. Students will consider how an analysis of the crossings of knots can provide information about their general classification. These ideas are related to others in graph theory in that certain knots can be embedded in graphs. One would like to characterize such graphs. Other topics include the calculation of topological characteristics called Betti numbers, vector-valued Hermitian forms arising in the differential geometry of Cauchy-Riemann structures and work in analytic number theory on the divisor problem for arithmetic progressions. Students will be recruited from the New England area. Efforts will be made see that the research continues after the summer ends. This will be particularly true of the students who are recruited from Williams College. It is expected that several publishable papers will result from the project and that some students will have the opportunity to present their work at professional meetings.