RTG: Geometry and Topology at the University of Virginia

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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.