Project Grant 2603921

The National Science Foundation Division of Mathematical Sciences awarded Duke University $103,300 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to fund research into complex geometry and differential invariants of period maps in algebraic geometry.

The recipient will conduct research on period maps, functions associated with families of geometric objects defined by polynomial equations, with applications to moduli problems in algebraic geometry. The work encompasses two main research tracks: half the projects continue a program studying period maps through their Fubini–Hodge forms, a class of differential invariants that includes Griffiths–Yukawa couplings, drawing analogy with the Hwang–Mok program for Fano manifolds. The remaining projects address the long-standing problem of developing analogs of the Ash–Mumford–Rapoport–Tai theory for arbitrary period maps. The principal investigator maintains an active mentoring program involving graduate student research and will continue efforts in proof formalization using artificial intelligence, creating opportunities at the undergraduate and graduate level.

Performance of research occurs at Duke University's Durham, North Carolina location. The award runs from September 1, 2026, through August 31, 2028. The award classification is a Project Grant, with the assistance type providing direct support for investigator-initiated research.