Title: Structural results in the Gromov-Witten theory of Calabi-Yau threefolds

Abstract: In this talk, I will explain how to prove structural predictions (made by physicists) about the higher-genus Gromov-Witten theory of Calabi-Yau threefolds X (in this talk, necessarily a scheme) which arise as hypersurfaces in weighted projective spaces by clever packaging of a virtual version of the Atiyah-Bott localization formula. This involves a moduli space introduced originally by (various subsets of) Chang-Guo-Li-Li-Liu which contains the moduli space of stable maps to X as a type of fixed locus under a torus action. A key tool for being able to perform calculations is a curious vanishing property of the virtual cycles of badly behaved connected components of the fixed locus.