RTG: Research Training in Geometry and Topology

RTG：几何和拓扑研究培训

• 批准号: 1745583
• 负责人: John Etnyre
• 金额: $ 213.04万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1745583&HistoricalAwards=false
• 关键词: RTG; Research; Training; Geometry; Topology

This project is designed to provide fertile ground for training undergraduate and graduate students as well as postdoctoral fellows through the Georgia Tech Geometry and Topology (GTGT) group, resulting in an increase in the number of U.S. citizens pursuing advanced research in geometry and topology. The project includes activities to stimulate interdisciplinary collaborations among mathematicians and engineers. The GTGT group's proximity to numerous institutions serving underrepresented groups in mathematics will be leveraged to increase the number of minorities and women studying mathematics. The project intends to develop students and postdoctoral fellows who become well-rounded scholars, accomplished teachers, and valuable members of the mathematical community. The GTGT group will provide comprehensive training to graduate students and postdocs through fellowships, expanded courses and seminars, and dedicated professional development activity. The GTGT group also will engage undergraduate students in REU projects, a directed reading program, and topics classes as well as in seminars about applying to graduate school. Each summer there will also be twelve summer REUs funded by the grant to provide a research capstone to the other undergraduate activities associated with the grant. The GTGT group will run a research conference each fall, allowing students and postdocs opportunities to interact with top researchers from around the country and to gain experience with organizing national activities. They will additionally run a biennial professional development workshop, undergraduate workshop, and summer school. It is expected that there will be significant interaction between trainees at all levels and that all parts of the project will work together to reinforce each other.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.

该项目旨在通过佐治亚理工学院几何与拓扑（GTGT）小组为培养本科生和研究生以及博士后提供肥沃的土壤，从而增加从事几何和拓扑高级研究的美国公民数量。该项目包括促进数学家和工程师之间跨学科合作的活动。GTGT小组靠近许多为数学领域代表性不足群体提供服务的机构，这将有助于增加少数族裔和女性学习数学的人数。该项目旨在培养学生和博士后，使他们成为全面发展的学者、有成就的教师和数学界有价值的成员。GTGT小组将通过奖学金、扩展课程和研讨会以及专门的专业发展活动，为研究生和博士后提供全面的培训。GTGT小组还将让本科生参与REU项目、定向阅读计划、主题课程以及有关申请研究生院的研讨会。每年夏天还将有12个夏季reu由拨款资助，为与拨款相关的其他本科生活动提供研究顶点。GTGT小组每年秋天将举办一次研究会议，让学生和博士后有机会与来自全国各地的顶尖研究人员互动，并获得组织全国性活动的经验。此外，他们还将举办两年一次的专业发展研讨会、本科生研讨会和暑期学校。预计各级受训者之间将有重要的互动，项目的所有部分将共同努力，相互加强。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

The Chebyshev–Frobenius homomorphism for stated skein modules of 3-manifolds

3-流形的规定绞丝模的切比雪夫-弗罗贝尼乌斯同态

• DOI: 10.1007/s00209-021-02904-6
• 发表时间: 2022
• 期刊: Mathematische Zeitschrift
• 影响因子: 0.8
• 作者: Bloomquist, Wade;Lê, Thang T.
• 通讯作者: Lê, Thang T.

Finite quotients of braid groups

辫子群的有限商

• DOI: 10.1007/s10711-019-00505-6
• 发表时间: 2020
• 期刊: Geometriae Dedicata
• 影响因子: 0.5
• 作者: Chudnovsky, Alice;Kordek, Kevin;Li, Qiao;Partin, Caleb
• 通讯作者: Partin, Caleb

Koszul duality in higher topoi

高等拓扑学中的科祖尔二元性

• DOI: 10.4310/hha.2023.v25.n1.a3
• 发表时间: 2023
• 期刊: Homotopy and Applications
• 作者: Beardsley, Jonathan;Péroux, Maximilien
• 通讯作者: Péroux, Maximilien

Representation stability in the level 4 braid group

4 级编织组中的表示稳定性

• DOI: 10.1007/s00209-022-03059-8
• 发表时间: 2022
• 期刊: Mathematische Zeitschrift
• 影响因子: 0.8
• 作者: Kordek, Kevin;Margalit, Dan
• 通讯作者: Margalit, Dan

An Alexander method for infinite-type surfaces

无限型曲面的 Alexander 方法

• 发表时间: 2022
• 期刊: New York journal of mathematics
• 影响因子: 0.6
• 作者: Roberta Shapiro