RTG: Geometry and Topology at UCLA

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Through a vertically integrated combination of research, training, and outreach activities, the Research Training Group project aims to increase the number of US citizens and residents who take part in research in mathematics at UCLA, with geometry, topology, and related computational methods as a focus. The researchers in the Geometry and Topology Group at UCLA work with a large cohort of postdocs, graduate students, and undergrads. This Research Training Group project aims to additionally support undergraduates, graduate students, and postdoctoral scholars in connecting with programs at UCLA and in the broader community that focus on K-12 education, on connecting with community colleges, and on integrating social justice concerns with mathematics. The project specifically seeks to support women and members of under-served groups in mathematical research.Three postdoctoral scholars and ten graduate students will be supported by this grant; they will be trained by the senior personnel in research topics such as algebraic topology, low-dimensional topology, differential geometry, symplectic geometry, algebraic geometry, and topological data analysis. Three research workshops will be conducted as part of this program: algebraic geometry, low-dimensional topology, and applied topology; the workshops, which will bring together experts in the field, aim to lead to new research and collaborations. A new seminar series will be created to create collaborations between pure and applied topologists. K-12 students will be trained through the UCLA Olga Radko Endowed Math Circle. In addition, expository mathematics articles will be written aimed at schoolchildren. A yearly research experience for undergraduates will be conducted involving local participants from the greater Los Angeles region, aiming to serve its large minority population. Community support will be created for undergraduate transfer students. Connections with nearby Cal State universities will be strengthened, and mentoring will be provided to their students. New courses will be created, including geometry and topology courses for lower division undergraduates. RTG-supported postdocs and graduate students will participate in many of these projects as mentors or docents.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.