Abstract

In mirror symmetry, we aim to build a relationship between the enumerative geometry of a symplectic manifold and period integrals on its mirror manifold. This relationship has been extended in the past 15 years to Landau-Ginzburg models. Roughly, a Landau-Ginzburg (LG) model is a triplet of data (X, G, W) where X is a quasi-affine variety, G is a group acting on X and W is a G-invariant complex-valued algebraic function from X to the complex numbers. Mirror symmetry relates the enumerative geometry of an LG model (so-called Fan-Jarvis-Ruan-Witten theory) to a system of oscillatory integrals on the mirror that serve as period integrals (so-called Saito-Givental theory). Recently, there has been progress in constructing open invariants on both sides of the mirror symmetry correspondence in these cases. We how this works for Fermat polynomials based on work with Mark Gross and Ran Tessler, with an emphasis on the period-style computations as they are more in line with the theme of the workshop.