Homological mirror functors via Maurer-Cartan formalism

This is a write-up of the lecture at String Math 2015. We give a survey on recent joint works with Hansol Hong and Siu-Cheong Lau where we develop a Lagrangian Floer theory formalism to explain some of Homological mirror symmetry phenomenons. The formalism does not need a Lagrangian torus fibration, but uses a single or finite collection of Lagrangians to produce a mirror Landau-Ginzburg model, which always comes with a canonical A(infinity)-functor from Fukaya category to matrix factorization category. We illustrate this by giving many different forms of the mirror of a symplectic torus.