Topics in Algebra

MATH 8174 Spring 2022

Course description

We will cover topics in Hodge theory from a variety of perspectives.

Schedule

MWF 12:20 PM -- 1:10 PM, KCEN S161 (you will need your campus ID to get to this room)

University of Colorado Academic Calendar

Office hours

M 10:00 AM -- 10:50 AM (remote), W 10:00 AM -- 10:50 AM (in person), Th 12:20 PM -- 1:10 PM (remote), or by appointment

Textbook

The textbook for the course is:

1. C.A.M. Peters and J.H.M. Steenbrink, Mixed Hodge Structures, Springer 2008.

Our treatment may also follow parts of:

1. (Complex Geometry) D. Arapura, Algebraic Geometry over the Complex Numbers, Springer 2012.
2. (Arithmetic Geometry) R. Hartshorne, Algebraic Geometry, Springer 1977.
3. (Complex Geometry) D. Huybrechts, Complex Geometry: an introduction Springer, 2005.
4. (Complex Geometry) P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley 1978.
5. (Complex Geoemtry) C. Voisin, Hodge Theory and Complex Algebraic Geometry, I, Cambridge 2002.
6. (PDE) R. Wells, Differential Analysis on Complex Manifolds (Third Edition), Springer 2008.

Grading

Grades will be based on homework and projects.