REU Site: Matrix Analysis, Combinatorics, and Applications

REU 网站：矩阵分析、组合学和应用

• 批准号: 1757603
• 负责人: Charles Johnson
• 金额: $ 25万
• 依托单位: College of William and Mary
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-05-01 至 2022-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1757603&HistoricalAwards=false
• 关键词: REU; Site; Matrix; Analysis; Combinatorics

The William and Mary Research Experiences for Undergraduates (REU) program seeks to initiate promising undergraduate students, from a variety of backgrounds, into productive mathematical research. This will also help to give them a useful preview of part of graduate study. In an 8-week program, carefully chosen students will be exposed to high-level, worthwhile problems in matrix analysis, combinatorics, and their applications and then mentored by experts in the process of making contributions to the understanding of these problems. The goal is two-fold: 1) to enable the students to perform sufficiently valuable research to warrant publication in respected outlets, and 2) to contribute materially to the body of knowledge about important areas of the mentioned subjects. Historically, the W&M REU program has involved quite a number of topics in this project. One of the unifying themes has been the interplay between combinatorial ideas and matrix analysis, often the role of combinatorial mathematics in the understanding of matrix analytical questions. This theme will continue. Some particular topic areas have been: 1) matrix completion problems, involving a variety of classes of matrices; 2) constraints on the multiplicities of the eigenvalues of a matrix, resulting from its graph; 3) the field of values of a matrix; 4) properties of matrices that may be inferred from the pattern of signs, or the zero/nonzero pattern of their entries; 5) totally positive matrices; and many other more specific questions. Each year, new problems are gathered from the active research programs of the principal investigators/mentors and their many collaborators.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.

威廉和玛丽研究经验的本科生（REU）计划旨在启动有前途的本科生，从各种背景，到富有成效的数学研究。这也将有助于给他们一个有用的预览部分研究生学习。在为期8周的课程中，精心挑选的学生将接触到矩阵分析，组合学及其应用中的高层次，有价值的问题，然后由专家指导，为理解这些问题做出贡献。目标是双重的：1）使学生能够进行足够有价值的研究，以保证在受人尊敬的网点发表，以及2）为上述主题的重要领域的知识体系做出重大贡献。从历史上看，W M REU计划在这个项目中涉及了相当多的主题。其中一个统一的主题是组合思想和矩阵分析之间的相互作用，通常是组合数学在理解矩阵分析问题中的作用。这一主题将继续下去。一些特殊的主题领域有：1）矩阵完备化问题，涉及各种类型的矩阵; 2）矩阵特征值的多重性的约束，由其图产生; 3）矩阵的值域; 4）可以从符号模式或其元素的零/非零模式推断的矩阵的性质; 5）完全正矩阵;以及其他一些更具体的问题。每年，新的问题是从主要研究者/导师和他们的许多合作者的积极研究计划收集。这个奖项反映了NSF的法定使命，并已被认为是值得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的支持。