Project Grant 2553961

The National Science Foundation Division of Mathematical Sciences awarded the University of Washington $180,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to support cutting-edge research in discrete geometry, specifically on convex polytopes and simplicial complexes. The project runs through July 31, 2029, with performance at the University of Washington in Seattle, Washington.

The research addresses long-standing problems and conjectures about face numbers and related invariants of convex polytopes, simplicial complexes, and related topological spaces. Work will focus on understanding which face-number sequences can occur and how algebraic, geometric, and topological structures restrict these possibilities. Research priorities include general convex polytopes that are neither simplicial nor simple, simplicial spheres with additional structure such as symmetry, simplicial balls, and spaces with singularities. The project will use and further develop tools from discrete geometry, commutative algebra, and algebraic geometry while strengthening connections between combinatorics and neighboring areas of mathematics. The award also supports the training of graduate students through involvement in research at the interface of combinatorics, geometry, and topology.