  We propose a mirror symmetry for 4d $\mathcal{N}=2$ superconformal field
theories (SCFTs) compactified on a circle with finite size. The mirror symmetry
involves vertex operator algebra (VOA) describing the Schur sector (containing
Higgs branch) of 4d theory, and the Coulomb branch of the effective 3d theory.
The basic feature of the mirror symmetry is that many representational
properties of VOA are matched with geometric properties of the Coulomb branch
moduli space. Our proposal is verified for a large class of Argyres-Douglas
(AD) theories engineered from M5 branes, whose VOAs are W-algebras, and Coulomb
branches are the Hitchin moduli spaces. VOA data such as simple modules, Zhu's
algebra, and modular properties are matched with geometric properties like
$\mathbb{C}^*$-fixed varieties in Hitchin fibers, cohomologies, and some DAHA
representations. We also mention relationships to 3d symplectic duality.
