For a knot in the 3-sphere, Heegaard Floer knot homology and instanton knot homology are both categorifications of its Alexander polynomial. Kronheimer-Mrowka conjectured that those two Floer homologies are indeed isomorphic over complex coefficients. In this talk, I'll first review definitions of both knot homologies, and then propose an approach to proving the isomorphism. This is joint work with Baldwin, Li, and Sivek. The first step of the approach has been done by Baldwin, Li, and I.
