Completions of Period Maps

Explore a comprehensive lecture on the completion and extension of period maps in algebraic geometry. Delve into the speaker's joint work with M. Green and P. Griffiths, which describes an extended period map with an image that forms a compact Moishezon variety. Examine the project's broader context, including collaborations with Radu Laza, to construct period mapping completions and their applications to moduli spaces. Compare this approach to classical cases involving minimal and maximal compactifications of period spaces. Investigate key technical inputs, including new results on the global structure of period maps at infinity, and how they extend consequences of Schmid's nilpotent orbit theorem. Discover how these structures, combined with the infinitesimal period relation and work by Cattani, Deligne, and Kaplan, allow for the application of Grauert's result on holomorphic equivalence relations to achieve the main result.