Federal Grant Award Summary

Ball State University received a $125,349 Project Grant from the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049), effective July 1, 2026 through June 30, 2029. The grant supports fundamental research in non-smooth geometry and analysis, extending classical calculus tools to study non-smooth functions, sets, abstract geometries, and fractal spaces. The principal investigator is developing new mathematical approaches to understand complex geometric objects through the construction and analysis of "coarse" and "pointwise" tangent fields for non-smooth sets in high-dimensional spaces, providing quantitative estimates and structural descriptions analogous to tangent planes on smooth surfaces.

The project delivers research contributions applicable across pure and applied mathematics and computer science, with particular relevance to problems in large data analysis, computational mathematics, and limiting cases of smooth problems. Beyond core research outputs, the grant includes broader impact activities emphasizing professional development of early-career researchers through organizational work within the analysis community and enhancement of the research environment at Ball State University through invited speakers, improved mentoring, and advising initiatives. This work contributes to advancing understanding of complex mathematical objects that arise across multiple scientific and computational domains.