questions like the nagata conjecture seek to determine when certain zero dimensional schemes impose independent conditions on sections of a line bundle on a surface. understanding analogous questions for vector bundles instead amounts to studying the birational geometry of moduli spaces of sheaves on a surface. we explain how to use higher-rank interpolation problems to compute the cone of effective divisors on any moduli space of sheaves on the plane. this is joint work with izzet coskun and matthew woolf.