The vertex functions are generating functions counting rational curves in a quiver variety. They give a basis of solutions to the quantum differential equation associated with the quiver variety. In my talk I discuss a construction of certain polynomial solutions of the quantum differential equations modulo a prime p. This construction is based on the so called 3D-mirror symmetry, which provides integral representations to the vertex functions.

In my talk I describe a number of conjectures relating the p-adic limits of these polynomial solutions to the vertex functions. The talk is based on a joint project with A. Varchenko arXiv:2302.03092