Thorgal Hinault, Caltech

Title: Decomposition and framing of F-bundles and applications to quantum cohomology

Abstract: In this talk, I will present the notion of F-bundle, an abstraction of the quantum D-module motivated by non-commutative Hodge structures. I will present two theorems: the spectral decomposition theorem, decomposing an F-bundle based on the eigenvalues of the action of the Euler vector field, and the extension of framing theorem, which allows to reconstruct isomorphisms between F-bundles. I will present applications of the theory of framing to the decomposition of the quantum D-module of a projective bundle and a blow-up. Based on arXiv:2411.02266, joint with Tony Yue Yu, Shaowu Zhang and Chi Zhang.