Quantum spectrum and Gamma structures for FJRW theory of general type


In this talk, I will explain quantum spectrum and asymptotic expansions in FJRW theory of invertible singularities of general type. Inspired by Galkin-Golyshev-Iritani’s Gamma conjectures for quantum cohomology of Fano manifolds, we propose Gamma conjectures for FJRW theory of general type. Here the Gamma structures are essential to understand the connection between algebraic structures of the singularities (such as Orlov’s semiorthogonal decompositions of matrix factorizations) and the analytic structures, such as asymptotic expansions in FJRW theory. The talk is based on the work joint with Ming Zhang.