Title: Tropical decomposition formula in log GLSM

Abstract: Log GLSM is a Gromov-Witten type theory which virtually counts curves in critical loci of certain given holomorphic functions, called superpotentials. In this talk, I will introduce a fundamental structural formula in log GLSM, called the tropical decomposition formula. On the Gromov-Witten side, this formula specializes to a quantum Lefschetz type formula, which computes Gromov-Witten invariants of complete intersections in terms of enumerative invariants of the ambient geometry and effective invariants depending on the superpotential. As an application, I will explain how this tropical quantum Lefschetz together with axioms of effective invariants can be used to establish a geometric polynomiality of Gromov-Witten generating functions of Calabi-Yau hypersurfaces in Fano four-folds for each g > 1. This is a joint work with Felix Janda and Yongbin Ruan.