Federal Project Grant Award Summary

Emory University received a $200,000 project grant awarded May 15, 2026, from the National Science Foundation's Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports fundamental research in spectral theory and scaling limits, with completion targeted for July 31, 2028. The research investigates mathematical properties of one-dimensional systems such as orthogonal polynomials and Schrödinger operators, focusing on how spectral properties behave at microscopic scales and how local eigenvalue distributions can be described through scaling limits of reproducing kernels. The project applies modern mathematical approaches based on de Branges canonical systems to develop optimal results in both fixed and varying measure settings.

The grant deliverables include original mathematical research contributions advancing understanding of universality phenomena and integrability in quantum and mechanical systems, with potential applications to random matrix theory and one-dimensional quantum mechanics. Additionally, the project provides structured research training opportunities for graduate students and postdoctoral scholars at Emory University's Atlanta, Georgia campus, contributing to workforce development in mathematical sciences. The research aims to characterize new scaling behaviors beyond standard universality classes and describe behaviors in critical and supercritical regimes of almost periodic and ergodic operators.