Torus links and colored Heegaard Floer homology

Link Floer homology is a filtered version of the Heegaard Floer homology defined for links in 3-manifolds. In this talk, we will introduce an algorithm to compute the link Floer homology of algebraic links from its Alexander polynomials. In particular, we give explicit descriptions of link Floer homology of torus link T(n, mn). As an application, we compute the limit of the link Floer homology when m goes to infinity, using certain cobordism maps, which can be used to define colored link Floer homology.  This talk includes joint work with Borodzik, Zemke, and with  Alishahi, Gorsky.