Persistent Homology, Metrics, and Applications on the Collection of Enriched Metric Measure Spaces

Edmonds, Ranthony A C, Columbus OH

Investigators

Abstract

This award is made as part of the FY 2021 Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowships, MPS-Ascend Program. Ranthony Edmonds is awarded this fellowship to conduct a program of research and education at the Ohio State University in the mathematical sciences, including applications to other disciplines, under the mentorship of the sponsoring scientist Facundo Memoli. This project is devoted to some challenging issues of topological data analysis (TDA), a new and rapidly growing field that leverages tools from algebraic topology and many other areas to study the shape of big data. Along with this research, Edmonds will develop educational activities related to data science in collaboration with existing partnerships with local and national networks focused on increasing representation of underrepresented minorities in the mathematical sciences. The project has several objectives. The first is the study of metric measure spaces, and finding an appropriate notion for the Gromov-Wasserstein (GW) distance. The second goal is to explore stability of data under small perturbations in the GW distance. The third goal is applied and concerns electoral redistricting where the basic idea is to use the GW metric to compare redistricting plans. 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.