Project Grant 2552947

The National Science Foundation Division of Mathematical Sciences awarded the President and Fellows of Harvard College $210,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to conduct research on the interactions of combinatorics and physics.

The award funds research addressing questions at the interface of combinatorics, algebra, and physics. In statistical physics, the project studies the relationship between the asymmetric simple exclusion process (ASEP) and families of polynomials in algebraic combinatorics, including interpolation polynomials, Macdonald polynomials, and Koornwinder polynomials; ASEP models traffic flow and protein synthesis translation and connects to the quantum transverse XY model. In quantum field theory, the project examines the combinatorics of the amplituhedron, a geometric object that computes scattering amplitudes measuring how massless particles interact in N=4 super Yang Mills theory. In mirror symmetry, the project applies polytopal mirror statements and cluster algebra technology to construct mirrors for positroid varieties in the Grassmannian. The research on ASEP carries potential applications to quantum information science by providing tools for studying quantum many-body phenomena, entanglement, and non-equilibrium dynamics. The award also supports the principal investigator's role as one of four editors of First Proof, an initiative assessing AI models' ability to prove mathematical statements, and training of graduate mathematicians.

Work is performed in Cambridge, Massachusetts. The project period runs from August 1, 2026, through July 31, 2028. This is a project grant.