REU Site: Algebra, Combinatorics, and Statistics

REU 网站：代数、组合学和统计学

• 批准号: 1757233
• 负责人: Yong Yang
• 金额: $ 26.97万
• 依托单位: Texas State University - San Marcos
• 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: 2018-09-01 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1757233&HistoricalAwards=false
• 关键词: REU; Site; Algebra; Combinatorics; Statistics

The Department of Mathematics at Texas State University will host an 8 week summer REU in the summers of 2019, 2020 and 2021, involving nine students per year working in teams of three under the supervision of a faculty mentor. The program will provide lodging, meals, transportation, as well as a stipend for all students. The chosen participants will come from a selective pool of applicants, and the program will directly involve them in research projects guided by faculty mentors. Beyond successful research outcomes the objectives of the program are to introduce students to aspects of mathematical research and the broader mathematical community. At the same time the students will develop mentoring relationships with faculty as they consider pursuing graduate degrees and a career in mathematics. Students will be part of an active community at Texas State; in addition to the REU there are a number of summer programs and world-renowned mathematicians who visit campus, and participants will be involved in various activities that bring students and faculty together. A diverse body of participants is strongly desired and priority will be given to applicants from groups that are underrepresented in the mathematical community. This includes minority students, women, as well as those students coming from institutions with limited resources to support independent research projects for their undergraduates.The research projects include a diverse collection of topics based on the research interests of the faculty mentors. Specific projects include commutative algebra arising from graphs and matroids, algebraic and combinatorial aspects of higher dimensional tilings, combinatorial problems arising from group theory, arithmetic properties of group invariants, linear and permutational representations of groups, statistical analysis on biological data, and survival analysis. Participants will spend some of the time learning the necessary background while pursuing original research. Students will be asked to present their findings in oral presentations, and will be guided in summarizing their work in a mathematical research paper. In the course of the program students will be trained in various skills including literature review, using software such as GAP, Macaulay2, and R to make and check examples, oral presentation skills, as well as written mathematical communication using Latex. Communication with the participants will continue after the program ends, and for instance students will be encouraged to present their work at local, regional, and national conferences in the subsequent academic year.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.

数学系在得克萨斯州州立大学将举办一个为期8周的夏季REU在2019年，2020年和2021年的夏天，涉及每年9名学生在一个教师导师的监督下，在三人一组的工作。 该计划将为所有学生提供住宿、膳食、交通以及津贴。被选中的参与者将来自一个有选择的申请人池，该计划将直接让他们参与由教师导师指导的研究项目。除了成功的研究成果，该计划的目标是向学生介绍数学研究和更广泛的数学界的各个方面。 与此同时，学生将发展与教师的指导关系，因为他们考虑攻读研究生学位和数学职业生涯。 学生将在得克萨斯州活跃的社区的一部分;除了REU还有一些暑期课程和世界知名的数学家谁访问校园，参与者将参与各种活动，使学生和教师在一起。 一个多元化的参与者是强烈希望和优先将给予申请人从群体中的数学界代表性不足。 这包括少数民族学生，妇女，以及那些来自资源有限的机构，以支持他们的本科生独立研究项目的学生。研究项目包括基于教师导师的研究兴趣的各种主题。 具体的项目包括交换代数所产生的图形和拟阵，代数和组合方面的高维tilings，组合问题所产生的群论，算术性质的群体不变量，线性和置换表示的群体，统计分析生物数据，生存分析。 参与者将花一些时间学习必要的背景知识，同时进行原创性研究。 学生将被要求在口头报告中介绍他们的研究结果，并将指导他们在数学研究论文中总结他们的工作。 在该计划的过程中，学生将接受各种技能的培训，包括文献综述，使用GAP，Macaulay 2和R等软件制作和检查示例，口头演示技能以及使用Latex进行书面数学交流。项目结束后，与参与者的交流将继续进行，例如，鼓励学生在下一学年的地方，地区和国家会议上展示他们的工作。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。

项目成果

The Prime Graphs of Some Classes of Finite Groups

• DOI: 10.1016/j.jpaa.2021.106990
• 发表时间: 2021-01
• 期刊: Journal of Pure and Applied Algebra
• 影响因子: 0.8
• 作者: Chris Florez;Jonathan Higgins;Kyle Huang;T. Keller;Dawei Shen;Yong Yang

Biconed Graphs, Weighted Forests, and $h$-Vectors of Matroid Complexes

双锥图、加权森林和拟阵复合体的 $h$ 向量

• DOI: 10.37236/9849
• 发表时间: 2021
• 期刊: The Electronic Journal of Combinatorics
• 作者: Cranford, Preston;Dochtermann, Anton;Haithcock, Evan;Marsh, Joshua;Oh, Suho;Truman, Anna
• 通讯作者: Truman, Anna

On the odd order composition factors of finite linear groups

• DOI: 10.1515/jgth-2019-0183
• 发表时间: 2020-06
• 期刊: Journal of Group Theory
• 影响因子: 0.5
• 作者: Alexander Betz;Max Chao-Haft;Ting Gong;A. Ter-Saakov;Yong Yang

A remark on a conjecture of Navarro and Tiep

对纳瓦罗和蒂普猜想的评论

• DOI: 10.1080/00927872.2022.2092630
• 发表时间: 2023
• 期刊: Communications in Algebra
• 影响因子: 0.7
• 作者: Gutierrez, Awildo;Huang, Yuqiao;Ngoc Hung, Nguyen;Peckham, Duncan;Yang, Yong
• 通讯作者: Yang, Yong

Completing and Extending Shellings of Vertex Decomposable Complexes

• DOI: 10.1137/21m1445119
• 发表时间: 2020-11
• 期刊: SIAM J. Discret. Math.
• 作者: Michaela Coleman;A. Dochtermann;Nathan Geist;Suho Oh