Link Floer homology and the stabilization distance
In this talk, we describe some applications of link Floer homology to the topology of surfaces in 4-space. If K is a knot in S^3, we will consider the set of surfaces in B^4 which bound K. This space is naturally endowed with a plethora of non-Euclidean metrics and pseudo-metrics. The simplest such metric is the stabilization distance, which is the minimum k such that there is a stabilization sequence connecting two surfaces such that no surface in the sequence has genus greater than k. We will talk about how link Floer homology can be used to give lower bounds, as well as some techniques for computing non-trivial examples. This is joint work with Andras Juhasz.