RTG: Geometry and Topology at UCLA

通过研究、培训和推广活动的垂直整合，研究培训小组项目旨在增加参加加州大学洛杉矶分校数学研究的美国公民和居民的数量，重点是几何、拓扑和相关计算方法。加州大学洛杉矶分校几何和拓扑学小组的研究人员与一大批博士后、研究生和本科生一起工作。这个研究培训小组的项目旨在另外支持本科生、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起来，这些项目侧重于K-12教育，联系社区学院，并将社会正义问题与数学相结合。该项目旨在支持女性和弱势群体的数学研究。三名博士后学者和十名研究生将得到这笔赠款的支持；他们将接受高级人员在代数拓扑学、低维拓扑学、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、低维拓扑学和应用拓扑学；这些研讨会将汇集该领域的专家，旨在促成新的研究和合作。将创建一个新的研讨会系列，以创建纯拓扑学家和应用拓扑学家之间的协作。K-12学生将通过加州大学洛杉矶分校奥尔加·拉德科捐赠数学圈接受培训。此外，还将针对小学生撰写数学说明性文章。每年将为本科生进行一次研究体验，参与者来自大洛杉矶地区，旨在服务于其庞大的少数族裔人口。为本科生转校生创建社区支持。与附近加州州立大学的联系将得到加强，并将为学生提供指导。将开设新课程，包括为低年级本科生开设的几何和拓扑学课程。RTG资助的博士后和研究生将作为导师或讲师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。

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.