Federal Project Grant Award Summary

The National Science Foundation's Division of Mathematical Sciences awarded $175,000 to Harvard College (President and Fellows of Harvard College) under the Mathematical and Physical Sciences program (CFDA 47.049) for a three-year project (July 1, 2026 – June 30, 2029) titled "Random Matrix Theory and Manifold Learning for High-Dimensional Data Integration." The project delivers new mathematical frameworks and computational tools designed to integrate high-dimensional datasets with partially shared structures by leveraging random matrix theory, manifold learning, and high-dimensional statistics. Key deliverables include theoretical advances in random matrix theory for composite and kernel matrices, a Procrustes-based framework for aligning low-dimensional structures in high-dimensional noise, and a kernel-spectral approach for joint nonlinear embedding. These methodological contributions will enable researchers to more accurately distinguish meaningful signals from noise when analyzing data from multiple sources.

The project addresses practical challenges across multiple sectors including molecular biology, precision medicine, business analytics, and economics, with particular emphasis on single-cell biology applications where understanding conserved cellular patterns across different conditions or species is critical. Broader impacts include development of open-source software tools and interdisciplinary training opportunities for students at various academic levels. The research will have applicability to analysis of electronic health records and large-scale biomedical or economic datasets, ultimately supporting more accurate, interpretable, and biologically relevant insights from integrated multi-source data analyses.