Instructor | Joj Helfer |
jhelfer (at) usc (dot) edu | |
Office Hours | MWF 12-1pm, by appointment (in KAP 464-B) |
All announcements will be posted on Blackboard.
Homework and lectures notes can be found on Overleaf.
Please let me know if you have any trouble accessing it.
The goal of this course is to learn about Hodge theory and some of its many interesting applications in complex algebraic geometry.
Most of the course will be devoted to covering the necessary general background in algebraic geometry, as well as studying various interesting examples. At the end of the course, students will present projects about further topics related to the course material.
Some of the basic algebraic geometry tools we will be covering include:
Some of the examples we will study include:
The main topics in Hodge theory we will cover are:
And here are some possible topics for the final project:
We will not be following any specific text, but will be making use of several references, primarily:
Here are some other good references which we may use:
All of these books are available online on the publisher’s website or through the USC library (links are provided above).
If you are interested in learning about the rich and fascinating history of algebraic geometry, I recommend:
Graduate level introductions to algebraic topology and differential geometry, especially differential forms and de Rham cohomology. It will be helpful to also have some familiarity with sheaves and with complex geometry/algebraic geometry/commutative algebra.
Homework will be assigned regularly. Solutions to homework problems will be required to be written with LaTeX. If you do not have experience with LaTeX and would like to learn how to use it, please ask the instructor.
The project will consist of an in-class 20-25 minute presentation on your chosen topic. These presentations will occupy the last portion of the course. The deadline to choose a topic (in consultation with the instructor) is Friday, February 9, and it will be required to submit a preliminary outline of the presentation by Friday, April 12.
The instructor’s office hours are TBA.
Any student requesting academic accommodations based on a disability is required to register with Disability Services and Programs (DSP) each semester A letter of verification for approved accommodations can be obtained from DSP. Please be sure the letter is delivered to me (or to TA) as early in the semester as possible. DSP is located in GFS 120 and is open 8:30 a.m.–5:00 p.m., Monday through Friday. Website for DSP (https://dsp.usc.edu/) and contact information: (213) 740-0776 (Phone), (213) 740-6948 (TDD only), (213) 740-8216 (FAX) dspfrontdesk@usc.edu.
USC seeks to maintain an optimal learning environment. General principles of academic honesty include the concept of respect for the intellectual property of others, the expectation that individual work will be submitted unless otherwise allowed by an instructor, and the obligations both to protect one’s own academic work from misuse by others as well as to avoid using another’s work as one’s own. All students are expected to understand and abide by these principles. SCampus, the Student Guidebook, contains the University Student Conduct Code (see University Governance, Section 11.00), while the recommended sanctions are located in Appendix A.
USC seeks to maintain an optimal learning environment. General principles of academic honesty include the concept of respect for the intellectual property of others, the expectation that individual work will be submitted unless otherwise allowed by an instructor, and the obligations both to protect one’s own academic work from misuse by others as well as to avoid using another’s work as one’s own. All students are expected to understand and abide by these principles. SCampus, the Student Guidebook, contains the University Student Conduct Code (see University Governance, Section 11.00), while the recommended sanctions are located in Appendix A.
In case of a declared emergency if travel to campus is not feasible, USC executive leadership will announce an electronic way for instructors to teach students in their residence halls or homes using a combination of Blackboard, teleconferencing, and other technologies. See the university’s site on Campus Safety and Emergency Preparedness.
This syllabus is not a contract, and the Instructor reserves the right to make some changes during the semester.