2025/2026

Research Seminar "An Introduction to Hodge Theory"

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

When: 3, 4 module

Open to: students of all HSE University campuses

Instructors: Alexei Gorinov

Language: English

Contact hours: 72

Course Syllabus

Abstract

The cohomology of every complex algebraic variety carries a mixed Hodge structure, which is a linear algebraic object that, as opposed to the cohomology itself, retains some (or sometimes all) information about the algebraic structure. For example, all smooth genus $g$ compact connected complex algebraic curves have isomorphic cohomology, but the mixed Hodge structure recovers the isomorphism type of the curve. In the seminar we will see how to construct this structure first for smooth compact varieties, then for just smooth varieties, and then in the general case. If time allows, we will also cover a more general viewpoint on the subject based on mixed Hodge modules.