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Title:
Hodge theory and moduli
Speaker:
Abstract:
Hodge theory provides a major tool for the study of moduli. Conversely, moduli have furnished a significant stimulus for the developement of Hodge theory. This talk will center around the questions • Q1 Torelli: To what extent does the Hodge structure on the cohomology H*(X) determine a smooth projective variety X? Better yet: How can one reconstruct X from Hodge theortic data associated to it? • Q2: To what extent does the structure of a completed image of the period mapping reflect the structure of a completed moduli space M? One knows a lot about how Hodge structures degenerate; can this be used to help understand the boundary M\M of moduli spaces?
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