The Gromov-Witten invariants are symplectic/algebraic invariants defined by counting curves. Their generating functions naturally satisfy some differential equations, and play a crucial role in 2D mirror symmetry. In this talk, I discuss a K-theoretic version of the Gromov-Witten invariants, and present my work on the generating function of genus-zero K-theoretic Gromov-Witten invariants of type-A partial flag varieties. Such generating function satisfies some q-difference equations and arise in 3D mirror symmetry instead. My method involves the idea of abelian/non-abelian correspondence and applies potentially to more general GIT quotients..

https://indico.math.cnrs.fr/event/16211/