Singularities in global pluripotential theory

In the study of the geometry of complex projective manifolds or compact Kähler
manifolds, it is important to understand a class of functions on these manifolds,
called quasi-plurisubharmonic functions. Traditionally, one is interested in regular
or mildly singular quasi-plurisubharmonic functions as the solutions to the
Monge—Ampère equations are usually regular. In recent years, it is gradually
realized that singular quasi-plurisubharmonic functions also play an important role.

In this talk, I will give a general introduction to the systematic study of the
singularities of quasi-plurisubharmonic functions carried out by Darvas, Di Nezza,
Lu and me in the last few years. In particular, I will explain the important notion of
good singularities and its various applications.