| Résume | The Landau-Ginzburg Calabi-Yau correspondence relates the quantum cohomology of a CY hypersurface X, with that of the associated singularity in the affine space. More precisely, both theories are encoded in generating I-functions, which match under analytic continuation and satisfy the Picard-Fuchs equation. In quantum K-theory, an analogue of quantum cohomology, the I-function of X satisfies a q-difference equation instead. In this talk, we will discuss an approach for K-theoretic invariants of the Fermat singularity, and explain how to recover all the solutions to the q-difference equation of the quintic threefold. |
