In a recent paper by Bazier-Matte and Schiffler, they discovered an unexpected connection between quiver representation and Alexander polynomial of links. Roughly speaking, under some specific restrictions, the F-polynomial of the quiver representation agrees with the Alexander polynomial. We are curious on whether such connection is also available for the knot Floer homology, which is the categorification of Alexander polynomial constructed by Ozsvath-Szabo and independently by Rasmussen.

In this talk, I will summarize the construction by Bazier-Matte-Schiffler and provide some evidences for the possibility of having an analogous connection for knot Floer homology.