Math 269Z: Topics in Hodge theory

Instructor: Salim Tayou

E-mail:, Office: Science Center 238. Canvas webpage.

Advancement of the class:




This course is an introduction to Hodge theory, which is a powerful framework for studying algebraic varieties and a very active area of research. We will start by introducing Hodge structures (pure and mixed), variations of Hodge structures, their period domains and degenerations of Hodge structures. Our next focus will be the study of Hodge loci. We will prove their algebraicity properties using tools from o-minimal geometry. Other topics may include: fields of definition of Hodge loci, Shimura varieties, and typical and atypical intersections.

Recommended books:

For the second part of the class, we will be following the proof of algebraicity of Hodge loci following this article: Further references include: More references will be added for the second part of the class.


Good background in complex analysis (Math 113), algebraic geometry (Math 232), differential geometry (Math 136), and algebraic topology (Math 231).

Exams and grading:

There will be weekly homework which will count for 80% of the final grade. No late homework will be accepted (except under special circumstances) and the lowest score will be dropped. Collaborative work on homework is accepted but you must write your own solution as well as the names of the collaborators. There will be a final project which consists of writing a short report on a topic tangentially treated in class and giving a 50 minute presentation about it. Together with participation, the final project will count for the remaining 20% of the grade.