Dano Kim, Canonical Bundle Formula and Degenerating Families of Volume Forms

We will talk about a metric version of Kawamata’s canonical bundle formula for log Calabi-Yau fibrations: the L² metric carries singularity described by the discriminant divisor and the moduli part line bundle has a singular hermitian metric with vanishing Lelong numbers. This answers a folklore conjecture arising from work of Kawamata and Tsuji and a question of Eriksson, Freixas i Montplet and Mourougane. It has immediate applications to L² extension theorems which was our starting point.