REU site: mathematical analysis and applications

The National Science Foundation Division of Mathematical Sciences awarded $366,029 to the University of Michigan-Dearborn on September 1, 2026, under the Mathematical and Physical Sciences program to operate a three-year Research Experience for Undergraduates (REU) site in mathematical analysis and applications.

The site will deliver an eight-week summer research program annually for eight undergraduate students, with recruitment prioritizing participants from institutions with limited research infrastructure, first-generation college students, and individuals lacking structured mathematical enrichment. The program integrates foundational mathematical areas—complex analysis, harmonic analysis, probability theory, and algebraic geometry—with computational methodologies from machine learning, data science, and statistics to address open problems including spectral analysis of CR manifolds using the Kohn Laplacian, robust machine learning models for biomedical data integration, and classification of error-correcting codes derived from toric varieties. Students will receive comprehensive professional development through a weekly speaker series covering mathematical careers across academia, industry, and national laboratories. The program culminates in the regional Summer Undergraduate Michigan Mathematics Research Conference, enabling students to present findings and establish mentorship relationships within the academic community.

The award runs through August 31, 2029, with performance at the University of Michigan-Dearborn campus in Dearborn, Michigan. The assistance type is a Project Grant.

Abstract

The research experience for undergraduates site in mathematical analysis and applications at the university of michigan-dearborn will provide an eight-week summer research program for eight undergraduate students annually over a three-year cycle. This project will recruit participants from different educational backgrounds, intentionally prioritizing students from institutions with limited research infrastructure, first-generation college students, and individuals who might otherwise lack structured mathematical enrichment. The program will expand the pipeline of capable researchers and strengthen the national scientific workforce, providing a strong public justification for the investment in these future innovators. Participants will experience comprehensive professional development through a weekly speaker series that highlights diverse mathematical careers across academia, industry, and national laboratories. The summer activities will culminate in the regional summer undergraduate michigan mathematics research conference, allowing students to disseminate their findings and establish long-term mentorship relationships within the broader academic community. The technical focus of the REU site will center on applying mathematical analysis to solve complex, real-world problems through experimentation, conjecture, and rigorous verification. The research framework will integrate foundational areas such as complex analysis, harmonic analysis, probability theory, and algebraic geometry with computational methodologies drawn from machine learning, data science, and statistics. Student cohorts will investigate a diverse array of open problems, including spectral analysis of CR manifolds using the kohn laplacian, development of robust machine learning models for biomedical data integration, and classification of error-correcting codes derived from toric varieties. Additional projects will encompass scalable phase retrieval algorithms for applied imaging, the optimization of groebner basis algorithms utilizing reinforcement learning, and advanced topological frameworks in mathematical music theory. Through computational testing and formal proof generation, students will contribute directly to the mathematical infrastructure, with the anticipated intellectual merit encompassing new algorithmic approaches, formal verifications, and original publications in peer-reviewed scientific journals. 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.- subawards are not planned for this award.