PRIMES PAIR: Partnering with AIM for Inclusive Research

该项目将通过德克萨斯州休斯敦圣托马斯大学的玛丽·弗拉格博士和美国数学研究所(AIM)的合作，在全国范围内促进本科生机构的研究(特别是那些为大量在数学科学劳动力中代表性不足的学生服务的机构)。弗拉格博士将与AIM合作，通过加强相对较新的(虚拟)AIM研究社区计划(在她共同组织的AIM研究社区中，教师加入合作研究小组，解决问题，并发表记录这些解决方案的论文)，支持教师研究和本科院校本科生的研究。她还将与AIM和数学计算与实验研究所(ICERM)合作，加强本科生学院的研究经验(RUEF)计划；她自己也是通过RUEF计划开始学习图论和线性代数的。参与这些项目的教师将与他们的教师研究相关的研究问题带到他们的课堂上。由于一半以上的本科数学学位是由没有博士学位的学院和大学授予的，因此这些机构的学生有机会从参与本科研究中受益至关重要。本科生研究在激发学生对数学科学研究生院和STEM劳动力的兴趣和为他们做好准备方面的重要性现在得到了广泛的认可。该项目还将直接扩大圣托马斯大学数学本科生的研究机会，并将在图论和线性代数的交叉点产生大量研究成果。线性代数方向围绕图的逆特征值问题(IEPG)。这一问题在包括动力学和物理在内的许多数学领域都有广泛的应用，在过去的几年里受到了极大的关注。作为该项目的一部分，弗拉格博士将组织一个由来自世界各地的专家研究人员组成的小组，在接下来的两年里在AIM上举行几次会议，通过应用分析工具在IEPG方面取得重大进展。零强迫是在IEPG的背景下引入的，但在量子系统控制和图搜索中也有应用。这项研究的图论方面的问题有许多应用，从线性代数到监控电网，图论的研究问题是该项目的重要组成部分。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project will promote research at undergraduate institutions (especially those that serve large numbers of students underrepresented in the mathematical sciences workforce) nationally through a partnership between Dr. Mary Flagg at the University of St. Thomas in Houston, TX and the American Institute of Mathematics (AIM). Dr. Flagg will work with AIM to support faculty research and research with undergraduate students at undergraduate institutions by enhancing the relatively new (virtual) AIM Research Communities program (in an AIM Research Community she co-organizes, faculty join collaborative research groups, solve problems, and publish papers documenting these solutions). She will also work with AIM and the Institute for Computational and Experimental Research in Mathematics (ICERM) to enhance the Research Experiences for Undergraduate Faculty (REUF) program; she herself got her start in graph theory and linear algebra through the REUF program. Faculty participating in these programs bring research problems connected to their faculty research into their classrooms. Because more than half of undergraduate mathematics degrees are awarded by colleges and universities that do not have doctoral programs, it is vitally important that students at these institutions have this opportunity to benefit from participating in undergraduate research. The importance of undergraduate research in stimulating interest in and preparing students for graduate school in the mathematical sciences and the STEM workforce is now widely recognized. This project will also directly expand research opportunities for undergraduate mathematics students at University of St. Thomas and will produce substantial research at the intersection of graph theory and linear algebra.The linear algebra direction is centered around the inverse eigenvalue problem for a graph (IEPG). This problem has broad applications in many areas of mathematics including dynamics and physics and has received a great deal of attention in the last few years. As part of this project, Dr. Flagg will organize a small group of expert researchers from around the world to meet several times at AIM over the next two years to make significant progress on the IEPG by applying tools from analysis. Zero forcing was introduced in the context of the IEPG, but also has applications in control of quantum systems and graph searching. Questions in the graph theory side of this research have many applications, from linear algebra to monitoring the power grid, and research questions in graph theory are a substantial part of the project.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.