206A, Winter 2020


Elham Izadi ; AP&M 6240 ; 858-534-2638 ; eizadi@math.ucsd.edu ; Office hours: 14:00-15:00 Mondays and Thursdays ;
Lectures: Tuesday, Thursday 11:00-12:20 AP&M 5829

Course description

This is an introduction to Hodge Theory.




Hodge Theory and Complex Algebraic Geometry, Volumes I and II, by Claire Voisin


Complex Geometry An Introduction, by Daniel Huybrechts
Principles of Algebraic Geometry, by Phillip Griffiths and Joseph Harris
A Survey of the Hodge Conjecture, by James Lewis
Period Mappings and Period Domains, by James Carlson, Stefan Müller-Stach and Christiaan Peters
Mixed Hodge Structures, by Christiaan Peters and Joseph Steenbrink (beware mistakes)
Mumford-Tate Groups and Domains: Their Geometry and Arithmetic, by Phillip Griffiths, Mark Green and Matthew Kerr
Hodge Theory, by Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths and Lê Dũng Tráng
A course in Hodge Theory, by Hossein Movasati


This course will feature student presentations. It is well known that the best way to learn something is to explain it to others. When we present something to others, we have to think about it in many different ways and look at it from different angles. Giving presentations is very difficult, which is why, when you give presentations, I will not judge your performance, but will help you learn the material in the best way possible and also help you learn how to give presentations. This is a skill that will be very useful in many different contexts, regardless of what your career goals are. Any comments will not affect your grade, but will help you learn.
Please prepare your presentations carefully. In particular, please write detailed typed notes for your presentations. It is usually a good idea to have a rehearsal with some of your friends/classmates before your presentation.

Some class notes:

01/07/2020 01/09/2020
01/14/2020 and 01/16/2020: Jacob's notes
01/21/2020 and 01/23/2020: Shubham's notes
02/11/2020 and 02/13/2020: Bochao's notes

Note that some adjustment to the above might be necessary during the quarter.
Elham Izadi Last modified: Thu May 14 13:12:52 PDT 2020