PRIMES PAIR: Partnering with AIM for Inclusive Research

PRIMES PAIR：与 AIM 合作开展包容性研究

• 批准号: 2331634
• 负责人: Mary Flagg
• 金额: $ 27.76万
• 依托单位: University of Saint Thomas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-15 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2331634&HistoricalAwards=false
• 关键词: PRIMES; PAIR; Partnering; AIM; Inclusive

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.

该项目将通过德克萨斯州休斯顿圣托马斯大学的玛丽·弗拉格博士和美国数学研究所 (AIM) 之间的合作，在全国范围内促进本科院校（特别是那些为数学科学劳动力中代表性不足的学生提供服务的院校）的研究。 Flagg 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，教师加入协作研究小组，解决问题并发表记录这些解决方案的论文），支持本科院校的教师研究和本科生研究。她还将与 AIM 和数学计算与实验研究所 (ICERM) 合作，增强本科生研究经验 (REUF) 项目；她本人就是通过 REUF 项目开始学习图论和线性代数的。 参与这些项目的教师将与其教师研究相关的研究问题带入课堂。由于一半以上的本科数学学位是由没有博士课程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。本科生研究对于激发学生对数学科学研究生和 STEM 劳动力的兴趣并为其做好准备的重要性现已得到广泛认可。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领域进行大量研究。线性代数方向以图的逆特征值问题（IEPG）为中心。这个问题在包括动力学和物理学在内的许多数学领域有着广泛的应用，并且在过去几年中受到了广泛的关注。 作为该项目的一部分，Flagg 博士将组织来自世界各地的一小群专家研究人员在未来两年内在 AIM 举行多次会议，通过应用分析工具在 IEPG 方面取得重大进展。 迫零是在 IEPG 的背景下引入的，但也在量子系统控制和图搜索方面有应用。这项研究的图论方面的问题有很多应用，从线性代数到监测电网，图论中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价值和更广泛的影响审查标准进行评估，被认为值得支持。