Hodge structures and variations

Abstract: We will first introduce Hodge structures, give some examples, and rephrase them as representations of the Deligne torus $\mathbb{S}$. Then we will talk about Hodge tensors, polarizations, and variations of Hodge structures. Finally, we will briefly introduce hermitian symmetric domains and realize them as parameter spaces for variations of Hodge structures.

Reference: Milne, Introduction to Shimura varieties, Chapter 2.

algebraic geometrynumber theory

Audience: advanced learners

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Fall 2025 topic: Weil conjectures.

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.