RTG: Geometry and Topology at UCLA

RTG：加州大学洛杉矶分校的几何和拓扑

• 批准号: 2136090
• 负责人: Sucharit Sarkar
• 金额: $ 250万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-01 至 2027-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2136090&HistoricalAwards=false
• 关键词: RTG; Geometry; Topology; UCLA

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.

通过研究，培训和推广活动的垂直整合组合，研究培训小组项目旨在增加美国公民和居民参加加州大学洛杉矶分校数学研究的人数，重点是几何，拓扑和相关的计算方法。加州大学洛杉矶分校几何与拓扑小组的研究人员与大量的博士后、研究生和本科生一起工作。该研究培训小组项目旨在进一步支持本科生，研究生和博士后学者与加州大学洛杉矶分校和更广泛的社区的项目联系，这些项目专注于K-12教育，与社区学院联系，并将社会正义问题与数学相结合。该项目特别致力于支持妇女和弱势群体的数学研究，将资助3名博士后学者和10名研究生，由高级人员对他们进行代数拓扑、低维拓扑、微分几何、辛几何、代数几何和拓扑数据分析等研究课题的培训。作为该计划的一部分，将举办三个研究研讨会：代数几何，低维拓扑和应用拓扑;研讨会将汇集该领域的专家，旨在开展新的研究和合作。一个新的研讨会系列将创建创建纯粹和应用拓扑学家之间的合作。K-12学生将通过UCLA Olga Radko Endowed Math Circle接受培训。此外，还将针对小学生编写临时数学文章。每年的本科生研究经验将进行涉及来自大洛杉矶地区的当地参与者，旨在服务于其庞大的少数民族人口。将为本科转学生提供社区支持。将加强与附近加州州立大学的联系，并为学生提供指导。新的课程将被创建，包括几何和拓扑课程，为低年级本科生。RTG支持的博士后和研究生将作为导师或讲解员参与其中的许多项目。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。