RTG: Geometry and Topology at the University of Virginia

该项目资助弗吉尼亚大学(UVA)博士后、研究生和本科生的研究培训，通过各种垂直连接的活动，将几何和拓扑学的数学主题结合在一起。该项目支持的主要活动是：扩大和正式的本科生研究计划；为研究生提供培训机会，使他们能够更多地沉浸在弗吉尼亚大学几何和拓扑学的创新研究课程中；增加几何/拓扑学博士后助理，既改善了系的研究环境，又受益于培训和指导机会；一系列年度会议，延续了最近成功的模式；UVA的几何和拓扑学研究范围包括稳定同伦理论和群上同调、更高代数结构的同伦理论、几何群论、双曲几何和特征变量、低维几何和拓扑学、规范理论和量子拓扑学。弗吉尼亚大学的所有6名几何/拓扑系组成了领导RTG项目的小组。在这些人中，两人是正教授，两人是副教授，两人是助理教授；两人是女性，三人在过去三年内进入了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一项受支持的活动招募有才华的候选人的优势。该项目允许对博士后助理和研究生进行几何学和拓扑学方面的强化培训，使他们能够制定自己的研究计划，并在弗吉尼亚大学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，他们将密切参与由这笔赠款支持的本科生研究。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所有阶段之间进行活跃的思想交流，为建立富有成效的合作关系提供环境，并在几何和拓扑学的现代研究方向上培训年轻的数学家和学生。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.