Infinitesimal extension of adjoint forms in Kähler setting and log injectivity theorem

In this talk, we will first establish a very general ddbar-lemma, together with a decomposition theorem for currents with values in a (singular) Hermitian line bundle. As a corollary, we will establish the Kähler version of an injectivity theorem due to O. Fujino in the projective case, as well as some results concerning the invariance of the plurigenera conjecture in the Kähler setting. This work is a collaboration with Mihai Paun.