Projectivity of the moduli space of KSBA stable pairs and applications

KSBA (Kollár-Shepherd-Barron-Alexeev) stable pairs are higher dimensional generalizations of (weighted) stable pointed curves. I will present a joint work with Sándor Kovács on proving the projectivity of this moduli space in characteristic zero, by showing that certain Hodge-type line bundles are ample on it. I will also mention applications to the subadditivity of logarithmic Kodaira dimension, and to the ampleness of the CM (Chow-Mumford) line bundle.