Title: Deformations and Variation of Hodge Structure
Speaker: Dan Simms
Abstract: Being defined topologically, cohomology is not strong enough to tell us anything about different complex structures we can put on a manifold. One way around this is to upgrade the cohomology with extra data, namely a Hodge structure. We’ll look at some deformation theory of how complex manifolds change in families, and what happens to the Hodge structures on their cohomology. As an application, we’ll hopefully have time to see a version of the Torelli theorem, which will let us recover many algebraic curves just from their Hodge structure.
Some snacks will be provided before and after the talk.