I shall motivate the generalised Monge-Ampere equations and formulate a conjecture (due to Lejmi and Szkelyhidi) about their solvability being equivalent to some numerical intersection criteria. I shall also illustrate the main ideas behind the proof of this conjecture in the projective case (joint work with Datar, based on the works by Demailly and Paun, and Gao Chen) by studying the Demailly-Paun-Nakai-Moizeshon criterion as a case study.

This is part 2 of 2 talks.