Link Floer spectrum via grid diagrams

Link Floer homology of links in S^3 can be computed as the homology of a grid chain complex defined using grid diagrams. I will describe a construction of a CW spectrum whose cells correspond to the generators of the grid chain complex, and whose cellular chain complex is the grid chain complex (and therefore, the homology is link Floer homology). This is joint with Ciprian Manolescu.