REU Site: The Williams College SMALL REU program

在威廉姆斯学院的小REU项目中，2009-2013年的夏天，大约23名本科生将在大约4人一组的时间里与大约6名教师一起进行原创性研究。 研究课题包括粘结、粒子碰撞拓扑、多变量连分式、局部环的完备化、随机矩阵理论、密度流形和等周问题、全局场的类群、遍历理论和各类随机矩阵的特征值分布。本REU的目标是向本科生介绍数学原创性研究的兴奋和挑战。 在这个过程中，学生们自然会学到很多背景知识，并被鼓励展示和发表他们的作品，这对研究生院来说都是无价的。数学活动的多样性为学生提供了丰富的智力环境。 我们的国家需要更广泛地欣赏和理解数学，不能遗漏任何人。 在过去的五年里，我们增加了参与该计划的妇女和少数民族的人数，我们正在继续寻找新的和更好的方法来鼓励妇女，少数民族，第一代大学生和其他代表性不足的群体的申请。 该提案的PI是女性，共同PI是西班牙裔。 学生，教师和更广泛的数学界将受益于原创研究的介绍和出版。学生将发展同龄人的终身网络，他们中的许多人将继续研究生学习，部分原因是他们的REU经验。

In the Williams College SMALL REU program, for nine weeks each summer, about 23 undergraduates will work in groups of about four on original research with about 6 faculty, for the summers 2009-2013. Topics of research include stick knots, topology of particle collisions, multivariable continued fractions, completions of local rings, random matrix theory, manifolds with density and isoperimetric problems, class groups of global fields, ergodic theory, and eigenvalue distribution of various classes of random matrices.The goal of this REU is to introduce undergraduates to the excitement and challenge of doing original research in mathematics. In the process, students naturally learn lots of background and are encouraged to present as well as publish their work, all invaluable for graduate school. The variety of mathematical activities provides a rich intellectual environment. Our nation needs a wider appreciation and understanding of mathematics, and cannot afford to leave anyone out. We have increased the numbers of women and minorities participating in the program over the last five years, and we are continuing to look for new and better ways to encourage applications from women, minorities, first generation college students, and other underrepresented groups. The PI for this proposal is a woman and the co-PI is Hispanic. Students, faculty and the broader mathematics community will benefit from the presentation and publication of original research. Students will develop a lifetime network of peers and many of them will pursue graduate studies, partially because of their REU experience.