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.

德克萨斯州立大学数学系将于 2019 年、2020 年和 2021 年夏季举办为期 8 周的夏季 REU，每年有 9 名学生在教师导师的监督下以三人一组的形式进行学习。 该计划将为所有学生提供住宿、膳食、交通以及津贴。选定的参与者将来自经过筛选的申请者，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之外，该计划的目标是向学生介绍数学研究的各个方面和更广泛的数学社区。 与此同时，学生在考虑攻读研究生学位和从事数学职业时，将与教师建立指导关系。 学生将成为德克萨斯州立大学活跃社区的一部分；除了 REU 之外，还有许多暑期项目和世界知名数学家访问校园，参与者将参与各种活动，将学生和教师聚集在一起。 强烈希望有多元化的参与者，并且将优先考虑来自数学界代表性不足的群体的申请人。 这包括少数族裔学生、女性以及来自资源有限的机构的学生，以支持其本科生的独立研究项目。研究项目包括基于教师导师的研究兴趣的各种主题。 具体项目包括由图和拟阵产生的交换代数、高维平铺的代数和组合方面、由群论产生的组合问题、群不变量的算术性质、群的线性和置换表示、生物数据的统计分析和生存分析。 参与者将花一些时间学习必要的背景知识，同时进行原创研究。 学生将被要求以口头报告的形式展示他们的发现，并指导他们在数学研究论文中总结他们的工作。 在课程中，学生将接受各种技能的培训，包括文献综述、使用GAP、Macaulay2和R等软件制作和检查示例、口头表达技巧以及使用Latex进行书面数学交流。项目结束后，与参与者的沟通将继续进行，例如，将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作品。该奖项反映了 NSF 的法定使命，并被认为值得通过以下方式获得支持：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。

项目成果

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: 2021-10
• 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

The prime graphs of some classes of finite groups

某些类有限群的素图

• DOI: 10.1016/j.jpaa.2021.106990
• 发表时间: 2022-07
• 期刊: Journal of Pure and Applied Algebra
• 影响因子: 0.8
• 作者: Florez, Chris;Higgins, Jonathan;Huang, Kyle;Keller, Thomas Michael;Shen, Dawei;Yang, Yong
• 通讯作者: Yang, Yong

Statistical and bioinformatic analysis of hemimethylation patterns in non-small cell lung cancer

非小细胞肺癌半甲基化模式的统计和生物信息学分析

• DOI: 10.1186/s12885-021-07990-7
• 发表时间: 2021-03-12
• 期刊: BMC Cancer
• 影响因子: 3.8
• 作者: Sun S;Zane A;Fulton C;Philipoom J
• 通讯作者: Philipoom J

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: 2023-01
• 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

On the odd order composition factors of finite linear groups

关于有限线性群的奇次组成因子

• DOI: 10.1515/jgth-2019-0183
• 发表时间: 2020-06-08
• 期刊: Journal of Group Theory
• 影响因子: 0.5
• 作者: Ale;er Betz;er;Max Chao;Ting Gong;A. Ter;Yong Yang
• 通讯作者: Yong Yang