This $210,001 federal Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research at Princeton University focused on exploring "local-to-global" phenomena in extremal and probabilistic combinatorics. The project aims to develop the theory of sublinear expander graphs to address central open problems in graph theory, matroid theory, and discrete geometry, including the Erdős-Gallai conjecture, Rota's basis conjecture, and the Erdős unit distance problem. The award will provide hands-on research opportunities for graduate students and potentially lead to the integration of findings into advanced courses. No subawards are planned under this grant, which runs from September 1, 2024 through August 31, 2027.
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