RTG: Geometry and Topology at the University of Virginia

RTG：弗吉尼亚大学的几何和拓扑

• 批准号: 1839968
• 负责人: Thomas Mark
• 金额: $ 249.82万
• 依托单位: University of Virginia Main Campus
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1839968&HistoricalAwards=false
• 关键词: RTG; Geometry; Topology; University; Virginia

This project funds research training for postdocs, graduate students, and undergraduate students at the University of Virginia (UVa), through a variety of vertically connected activities united by the mathematical themes of geometry and topology. The major activities supported by this project are: an expanded and formalized program of undergraduate research; traineeships for graduate students that allow greater immersion in the innovative research-directed coursework in geometry and topology at UVa; additional geometry/topology postdoctoral associates that both enhance the research environment of the department and benefit from training and mentorship opportunities; a series of annual conferences continuing a recent successful model; and a regional collaborative research initiative that brings graduate students, postdocs and faculty from UVa and regional schools together in teams for intensive training and collaboration aimed at particular problems in geometry or topology.The scope of research in geometry and topology at UVa includes stable homotopy theory and group cohomology, homotopy theory of higher algebraic structures, geometric group theory, hyperbolic geometry and character varieties, low-dimensional geometry and topology, gauge theory, and quantum topology. All 6 geometry/topology faculty at UVa form the group leading the RTG project. Of these, two are full professors, two associate professors and two assistant professors; two are women and three joined the UVa math department within the last three years. This diversity of research interest, seniority, and background will be an advantage in recruiting talented candidates for each of the supported activities. The enhanced training for postdoctoral associates and graduate students in geometry and topology allowed by this project will enable them to develop their own research programs and establish robust professional networks outside of the UVa mathematics department. The project will also provide essential mentoring experience for postdocs and graduate students, who will be closely involved in undergraduate research supported by this grant. The variety of conferences and research activities supported by this project will enable a lively exchange of ideas between active researchers in all stages of their careers, provide a milieu for forging productive collaborative relationships, and train younger mathematicians and students in the modern research directions of geometry and topology.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.

该项目资助弗吉尼亚大学（UVa）的博士后，研究生和本科生的研究培训，通过几何和拓扑的数学主题联合的各种垂直连接的活动。该项目支持的主要活动是：本科生研究的扩大和正规化计划;研究生的培训，使更多的沉浸在创新的研究导向的课程在几何和拓扑在弗吉尼亚大学;额外的几何/拓扑博士后联营公司，既提高了部门的研究环境，并受益于培训和导师的机会;一系列年度会议，延续最近的成功模式;以及一个区域性的合作研究项目，博士后和教师从UVa和区域学校一起在团队中进行密集的培训和合作，旨在解决几何或拓扑学中的特定问题。在UVa包括稳定的同伦理论和群上同调，同伦理论的高级代数结构，几何群论，双曲几何和字符品种，低维几何和拓扑，规范理论，和量子拓扑。UVa的所有6个几何/拓扑教师组成了领导RTG项目的小组。其中，两名是正教授，两名副教授和两名助理教授;两名是妇女，三名在过去三年内加入弗吉尼亚大学数学系。这种研究兴趣，资历和背景的多样性将是为每个支持的活动招募有才华的候选人的优势。该项目所允许的几何和拓扑学博士后助理和研究生的强化培训将使他们能够开发自己的研究计划，并在UVa数学系之外建立强大的专业网络。该项目还将为博士后和研究生提供必要的指导经验，他们将密切参与该补助金支持的本科生研究。该项目支持的各种会议和研究活动将使活跃的研究人员在其职业生涯的各个阶段之间进行生动的思想交流，为建立富有成效的合作关系提供环境，该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的学术价值和更广泛的影响审查标准。

项目成果

A horn-like characterization of the fibrant objects in the minimal model structure on simplicial sets

单纯集上最小模型结构中纤维物体的喇叭状表征

• 发表时间: 2023
• 期刊: Higher structures
• 作者: Feller, Matt

Stable homotopy refinement of quantum annular homology

量子环同调的稳定同伦细化

• DOI: 10.1112/s0010437x20007721
• 发表时间: 2021
• 期刊: Compositio Mathematica
• 影响因子: 1.8
• 作者: Akhmechet, Rostislav;Krushkal, Vyacheslav;Willis, Michael
• 通讯作者: Willis, Michael

Effective generation of right-angled artin groups in mapping class groups

映射类群中直角artin群的有效生成

• DOI: 10.1007/s10711-021-00615-0
• 发表时间: 2021
• 期刊: Geometriae Dedicata
• 影响因子: 0.5
• 作者: Runnels, Ian

Theorem A for marked 2-categories

标记 2 类别的定理 A

• DOI: 10.1016/j.jpaa.2022.107040
• 发表时间: 2022
• 期刊: Journal of Pure and Applied Algebra
• 影响因子: 0.8
• 作者: Abellán García, Fernando;Stern, Walker H.
• 通讯作者: Stern, Walker H.

2-Segal objects and algebras in spans

2-Segal 对象和跨度代数

• DOI: 10.1007/s40062-021-00282-8
• 发表时间: 2021
• 期刊: Journal of Homotopy and Related Structures
• 影响因子: 0.5
• 作者: Stern, Walker H.