Federal Grant Award Summary

The University of Maryland, College Park received a $355,201 Project Grant from the National Science Foundation's Division of Mathematical Sciences (CFDA 47.049, Mathematical and Physical Sciences) awarded on October 1, 2025, with completion targeted for June 30, 2026. The project investigates higher classification theory in model theory with applications to complex mathematical structures. Specifically, the research extends existing model-theoretic techniques from binary structures (graphs) to higher-arity structures (hypergraphs), which provide mathematical frameworks for describing complex networks where interactions occur simultaneously among multiple nodes rather than between pairs of nodes alone.

The core deliverables include advancing infinitary model-theoretic methods to address combinatorial problems in geometrically and algebraically derived hypergraphs, while applying combinatorial findings to open questions in model theory. The project leverages Shelah's classification program to identify combinatorial dividing lines that distinguish between structurally tame and untamed mathematical objects, enabling dramatic improvements in graph combinatorial results when restricted to tame structures. The grant incorporates educational components through training of graduate and undergraduate students, supporting workforce development in mathematical sciences consistent with the NSF's emphasis on integrating research with education.