Research Initiation Award: Toward Understanding Persistent Homology in Topological Data Analysis

HBCU-UP的研究启动奖为STEM教师提供支持，以开展研究活动，进一步提高他们的研究能力和有效性，并帮助加强HBCU的研究和教学。克拉克亚特兰大大学的这一奖项有可能推进拓扑数据分析，显着改善健康结果，培养计算机编程和数据科学的本科生，并为课程制作先进的技术教育模块。这个项目是重要的，因为结果可能有广泛的应用到一些领域和工作是必要的，以推进拓扑数据分析的潜力，重点是如何组织，结构化和连接空间。该项目将在几何和拓扑学的交叉点上培训HBCU的本科学生。该项目旨在产生结果，从而开发实用的数学工具，通过加强其与统计学和机器学习的联系来促进我们对持久同源性的理解。一旦这些工具存在，它们可能会被应用于各种应用，包括经济学，生物学，医学，政治学，化学和图像分析;从而增加公众对数学的参与。本项目中提出的研究和教育活动旨在为少数群体的学生提供机会，使他们能够从事多学科研究，成为有竞争力的、非常适合进入研究生院并最终成为劳动力的候选人。该项目将积极促进和鼓励历史上在数学科学中代表性不足的群体的学生的保留。该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

HBCU-UP’s Research Initiation Awards provide support for STEM faculty to pursue research activities to further their research capabilities and effectiveness and help enhance research and teaching at HBCUs. This award to Clark Atlanta University has the potential to advance topological data analysis that significantly improve health outcomes, train undergraduate students in computer programming and data science, and produce advanced technology education modules for courses. This project is significant in that the results may have broad applications to a number of fields and the work is necessary to advance the potential of topological data analysis, which focuses on how spaces are organized, structured, and connected. The project will train undergraduate HBCU students in data science at the intersection of geometry and topology. The project aims to produce results that will lead to the development of practical mathematical tools to advance our understanding of persistent homology by bolstering its connection to statistics and machine learning. Once these tools exist, they may be applied to a diverse set of applications, including economics, biology, medicine, politics, chemistry, and image analysis; thereby increasing public engagement with mathematics. The research and educational activities proposed in this project aim to provide opportunities for students from minoritized groups to engage in multidisciplinary research and become competitive, well-suited candidates for graduate school and ultimately, the workforce. This project will positively contribute to and encourage the retention of students from historically underrepresented groups in mathematical sciences.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.