Noncommutative Homological Mirror Functor

We formulate a constructive theory of noncommutative Landau-Ginzburg models mirror to symplectic manifolds based on Lagrangian Floer theory. The construction comes with natural functor from the Fukaya category matrix factorizations constructed model. As applications, it is applied elliptic orbifolds, punctured Riemann surfaces and certain non-compact Calabi-Yau threefolds construct their mirrors functors. In particular recovers strengthens several interesting results Etingof-Ginzburg, Bocklandt Smith, gives unified understanding in terms symmetry geometry. an application, we explicit global deformation quantization affine del Pezzo surface as orbifold.