Riemann-Hilbert correspondence for $q$-difference modules

I will propose a formulation of Riemann-Hilbert correspondence for holonomic $q$-difference equations in arbitrary many variables, in the case $|q|<1$. The answer is given in terms of Fukaya categories of rational Lagrangian cones, and coherent sheaves on the power of an elliptic curve. The limiting case $|q|=1$ also make sense, giving infinitely many algebraic structures on the same analytic stack. If the time permits, I'll speculate about general Torelli theorem for complex analytic noncommutative spaces (joint work in progress with Y.Soibelman).