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

HBCU-UP的研究启动奖为STEM教师开展研究活动提供支持，以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。授予克拉克·亚特兰大大学的这一奖项具有推动拓扑数据分析的潜力，这些分析显著改善了健康状况，培训了计算机编程和数据科学方面的本科生，并为课程制作高级技术教育模块。该项目具有重要意义，因为其结果可能在许多领域具有广泛的应用，而且这项工作对于促进拓扑数据分析的潜力是必要的，拓扑数据分析的重点是空间是如何组织、结构和连接的。该项目将为HBCU的本科生提供几何学和拓扑学交叉领域的数据科学方面的培训。该项目的目的是产生将导致开发实用数学工具的结果，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一系列不同的应用，包括经济、生物、医学、政治、化学和图像分析；从而增加公众对数学的参与。本项目建议的研究和教育活动旨在为来自小规模群体的学生提供从事多学科研究的机会，并成为具有竞争力的、非常适合研究生院并最终成为劳动力的候选人。这个项目将积极地帮助和鼓励来自历史上代表性不足的群体的学生留在数学科学领域。这个奖项反映了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。

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.