Federal Grant Award Summary

California Institute of Technology (Caltech) received a $300,000 Project Grant from the National Science Foundation's Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049), effective July 1, 2026, through June 30, 2031. This CAREER award supports foundational research on random discrete systems, including random graphs and related probabilistic phenomena. The project will develop new mathematical techniques to address fundamental gaps in understanding threshold phenomena and first moment obstructions, with extensions to applied settings such as random subspaces of finite vector spaces relevant to cryptography applications.

The award encompasses research, education, and workforce development components. Key deliverables include development of new mathematical toolkits for probabilistic analysis, peer-reviewed publications advancing theoretical understanding of random systems, and educational products including new courses, lecture notes, and tutorials. Additionally, the project will strengthen connections between mathematics and computer science through conferences and summer schools, and will provide mentoring and training opportunities for graduate, undergraduate, and high school students. The research outcomes are intended to strengthen mathematical foundations for large networks and random systems with applications to artificial intelligence and quantum information science.