Mixed Period Maps: Definability and Algebraicity

Explore the intricacies of mixed period maps and their definability and algebraicity in this 56-minute lecture by Jacob Tsimerman from the University of Toronto. Delve into the development of o-minimal geometry with nilpotents, known as "definable analytic spaces," and understand how this theory proves a definable GAGA statement. Learn about Griffiths' conjecture on the algebraic nature of period map images and its proof. Examine the o-minimal approach in the context of variations of mixed Hodge structures and discover a generalization of Griffiths' conjecture. Cover topics such as mixed Hodge structures on varieties, moduli spaces, definability concepts, the main theorem, polarization, theta bundles, and bi-extension bundles in this comprehensive exploration of advanced mathematical concepts.

Intro
Mixed Hodge structures on Varieties
Moduli spaces of mixed Hodge structures
Definability: Basic setup
Definability: Splittings
Definability: Retractions
Definability: Key Theorem
Main theorem
An example of mixed Hodge structures
The polarization
One weight at a time
The theta bundle
Bi-extension Bundle
To finish