The topic concerns the variation of the Bergman spaces themselves. This is closely related to part 1, but more general. It is most naturally formulated in the setting of complex manifolds and line bundles over them and closely related to classical topics in algebraic geometry like variations of Hodge structures, and Kahler geometry.

   The above two lectures are based on: arXiv:math/0505469 Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains and arXiv: 1002.4797 Strict and non strict positivity of direct image bundles