Lagrangian Floer theory in symplectic manifold associate a category (A infinity category) to a symplectic manifold. More than 20 years ago a relation of a relation between Lagrangian Floer theory and Gauge theory was studied by Floer himself various other people. A conjecture by Atiyah and Floer is based on this relation. One motivation of introducing A infinity category associated to a Symplectic manifold is to study Atiyah-Floer conjecture and related problems. In this talk, based on a joint work with A. Daemi, I want to explain some of the recent progress in this problem.
