Federal Grant Award Summary

The National Science Foundation (NSF) Division of Mathematical Sciences awarded $353,016 to the University of Florida under the Mathematical and Physical Sciences program (CFDA 47.049) for a five-year CAREER grant project running from July 1, 2026, through June 30, 2031. The award supports fundamental research advancing the geometric theory underlying persistent homology, a computational tool for analyzing the shape and structure of high-dimensional datasets. The investigator will develop theoretical foundations for Vietoris-Rips and Čech complexes applied to finite datasets and manifolds, with applications to bounding Gromov-Hausdorff distances between metric spaces. This work directly supports machine learning and artificial intelligence applications where understanding data geometry is essential for developing interpretable, trustworthy algorithms across multiple scientific disciplines.

In addition to core research activities, the project emphasizes broader community engagement through the development of online seminars and educational content designed to support undergraduate researchers and their mentors within the applied topology community. No sub-awards are planned for this project. The research addresses a critical need to establish rigorous mathematical foundations for data shape analysis techniques, enabling scientists to confidently apply persistent homology methods and validate their analytical conclusions from complex, nonlinear, high-dimensional, and noisy datasets across multiple scales.