Math Graduate Student Seminar

Gromov–Witten invariants are (virtual) curve counts, and a convenient way to package them is via the quantum differential equation. This viewpoint arises naturally in mirror symmetry, relating curve counting on the A-side to singularity theory on the B-side. A geometric framework for organizing these structures is provided by F-bundles, a non-Archimedean analogue of Frobenius manifolds. In this talk, we will discuss our recent work on a non-Archimedean decomposition theorem for F-bundles, building on Hinault–Yu–Zhang–Zhang (2024), as well as the construction of "Hodge atoms" as birational invariants, following Katzarkov–Kontsevich–Pantev–Yu (2025) and their application to the irrationality of cubic fourfolds.