Abstract: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.