Nakamaye's theorem on complex manifolds

A well-known result of Nakamaye states that the augmented base locus of a nef and big line bundle on a smooth projective variety over the complex numbers equals its null locus. I will discuss an extension of this theorem to all nef and big real (1,1) classes on compact complex manifolds, which also gives an analytic proof of Nakamaye's original result. I will also mention some consequences of this theorem, and some recent further developments. This is joint work with Tristan Collins.