Quantum Field Theory and Mirror Symmetry

I will talk about three domains in mirror symmetry where QFT is used: 1. Limit points of the moduli space of QFT and the birth of mirror symmetry; 2. The passage from the theory of type A (Gromov-Witten on a toric variety) to the mirror theory of type B at the level of quantum field theory; 3. Tropical mirror symmetry and BCOV field theory.