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.

该项目旨在为培训本科生和研究生以及通过佐治亚技术的几何学和拓扑（GTGT）小组提供肥沃的基础，从而增加了从事几何学和拓扑的美国公民的数量。该项目包括刺激数学家和工程师之间跨学科合作的活动。 GTGT集团与众多在数学中代表性不足的群体服务的机构的距离将被利用，以增加学习数学的少数民族和妇女的数量。该项目旨在发展学生和博士后研究员，他们成为全面的学者，有成就的老师和数学社区的宝贵成员。 GTGT小组将通过奖学金，扩大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小组还将与本科生参与REU项目，有指导的阅读计划以及主题课程以及有关申请研究生院的研讨会。每年夏天，还将有十二个由赠款资助的夏季Reus，以向与赠款相关的其他本科活动提供研究顶峰。 GTGT小组每年秋天将举办一个研究会议，使学生和博士后机会与来自全国各地的顶级研究人员进行互动，并获得组织国家活动的经验。他们还将举办两年一的专业发展研讨会，本科研讨会和暑期学校。可以预期，各级学员之间会有很大的互动，并且该项目的所有部分都将共同加强彼此。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子和更广泛影响的评估审查标准的评估来获得支持的。

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