206A, Fall 2022


Elham Izadi ; AP&M 6240 ; 858-534-2638 ; eizadi@math.ucsd.edu ;
Office hours: 11:00-12:00 Tuesdays and Thursdays in AP&M 5218, I would very much appreciate if you could let me know in advance if you are planning to come to office hours;
Lectures: Tuesday, Thursday 9:30-10:50 AP&M 5402

Course description

We will learn about some applications of 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
Abelian varieties, by David Mumford
Complex tori and abelian varieties, by Olivier Debarre
Complex abelian varieties, by Christina Birkenhake and Herbert Lange
More references can be found in the notes below


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:

Preliminary notes

Topics for presentations:

(1) Period domains
(2) Mumford-Tate groups and domains
(3) Challenge: What is an admissible normal function?
(4) Deligne cohomology and the normal function of a primitive Hodge class
(5) Some deformation theory
(6) The proof of Voisin's formula

Note that some adjustment to the above might be necessary during the quarter.
Elham Izadi Last modified: Thu Oct 20 13:44:08 PDT 2022