REU Site: UCSB Mathematics Summer Research Program for Undergraduates

REU 网站：UCSB 本科生数学暑期研究计划

• 批准号: 1850663
• 负责人: Maria Isabel Bueno Cachadina
• 金额: $ 34.77万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-06-15 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1850663&HistoricalAwards=false
• 关键词: REU; Site; UCSB; Mathematics; Summer

The UCSB Mathematics Summer Research Program for Undergraduates aims to provide a full research experience to undergraduate students in mathematics from different backgrounds. Over the course of the eight-week program, the students will learn to investigate and solve open problems in diverse areas of mathematics, to work in a collaborative environment, to communicate their mathematical results through talks and written reports, and to publish their findings in appropriate journals with the goal of disseminating their research. The program will expose the participants to daily life in graduate school, through interactions with graduate students, graduate advisors, faculty and postdocs in the UCSB math department. In addition, through professional development workshops, the participants will learn about different areas in industry that demand professionals with good research skills. Historically, the UCSB REU has not focused on a specific area of mathematics. However, the program intends to be accessible to students with a variety of backgrounds in mathematics. Thus, the research projects are likely to be in linear algebra, matrix analysis, numerical linear algebra, combinatorics and graph theory; that is, in areas that do not require extensive mathematical background from students. Examples of topics that have been studied in this program before include 1) primitive circulant matrices; 2) matrix polynomials and linearizations; 3) matrix equations; 4) parking functions; 5) Alexander and Jones polynomials; 6) sequential dynamical systems. The topics will change every year depending on the active research areas of the mentors involved in the program. The final goal is to expose the students to the techniques and methods used to tackle problems in these areas, to publish papers in refereed professional journals, and to participate and give talks in conferences for undergraduates. The REU concludes with a poster conference in which undergraduates doing summer research in all the UCSB departments present their results and make it accessible to non-experts in the area. Previous projects and publications as well as more information about the program can be found on the website http://math.ucsb.edu/REU.This site is supported by the Department of Defense in partnership with the NSF REU program.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.

UCSB数学暑期研究项目旨在为来自不同背景的数学本科生提供全面的研究经验。在为期八周的课程中，学生们将学习调查和解决不同数学领域的开放问题，在协作环境中工作，通过演讲和书面报告交流他们的数学结果，并在适当的期刊上发表他们的发现，以传播他们的研究成果。该项目将通过与UCSB数学系的研究生、研究生导师、教师和博士后的互动，让参与者接触研究生院的日常生活。此外，透过专业发展工作坊，参加者将了解不同行业需要具备良好研究技能的专业人士。从历史上看，UCSB REU并没有专注于特定的数学领域。然而，该计划旨在为具有各种数学背景的学生提供机会。因此，研究项目可能是线性代数、矩阵分析、数值线性代数、组合学和图论；也就是说，在不需要学生广泛的数学背景的领域。本课程之前研究过的主题包括：1)原始循环矩阵；2)矩阵多项式和线性化；3)矩阵方程；4)停车功能；5)亚历山大和琼斯多项式；顺序动力系统。每年的主题将根据参与该计划的导师的活跃研究领域而变化。最终目标是让学生接触到解决这些领域问题的技术和方法，在专业期刊上发表论文，参加本科生会议并发表演讲。REU最后举办了一个海报会议，在会上，在UCSB所有院系做暑期研究的本科生将展示他们的研究成果，并向该领域的非专家开放。以前的项目和出版物以及有关该计划的更多信息可以在网站http://math.ucsb.edu/REU.This上找到，该网站由国防部与NSF REU计划合作提供支持。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Linearizations for Interpolatory Bases - a Comparison: New Families of Linearizations

插值基的线性化 - 比较：线性化的新系列

• DOI: 10.13001/ela.2020.5183
• 发表时间: 2020
• 期刊: The electronic journal of linear algebra
• 作者: M. I. Bueno, A. Ashkar

ALMOST ABELIAN LIE GROUPS, SUBGROUPS AND QUOTIENTS

几乎阿贝尔李群、子群和商

• DOI: 10.1007/s10958-022-05872-2
• 发表时间: 2022
• 期刊: Journal of Mathematical Sciences
• 作者: Rios, Marcelo Almora;Avetisyan, Zhirayr;Berlow, Katalin;Martin, Isaac;Rakholia, Gautam;Yang, Kelley;Zhang, Hanwen;Zhao, Zishuo
• 通讯作者: Zhao, Zishuo

On why using $${{\mathbb {D}}}{{\mathbb {L}}}(P)$$ for the symmetric polynomial eigenvalue problem might need to be reconsidered

为什么可能需要重新考虑使用 $${{mathbb {D}}}{{mathbb {L}}}(P)$$ 来解决对称多项式特征值问题

• DOI: 10.1007/s10092-022-00483-4
• 发表时间: 2022
• 期刊: Calcolo
• 影响因子: 1.7
• 作者: Bueno, M. I.;Pérez, J.;Rogers, S.
• 通讯作者: Rogers, S.

Linear maps preserving the Lorentz spectrum: the $2 \times 2$ case

保留洛伦兹谱的线性映射：$2 imes 2$ 情况

• DOI: 10.13001/ela.2022.6925
• 发表时间: 2021
• 期刊: The Electronic Journal of Linear Algebra
• 作者: Bueno, María I.;Furtado, Susana;Klausmeier, Aelita;Veltri, Joey
• 通讯作者: Veltri, Joey