PL-surfaces in homology 4-balls

Consider manifold-knot pair (Y, K) where Y is an integer homology sphere and K is a knot inside Y. In the joint work with Jen Hom and Matt Stoffregen, we proved that the minimum genus of a PL-surface bounded by K can be arbitrarily large in any bounding homology 4-ball. The proof uses Heegaard Floer homology. I will also talk about other related results.