| Lectures: | MWF 1:30--2:20 Sieg 231 |
| Instructor: | Jack Lee Padelford C-546 543-1735 E-mail: lee@math.washington.edu Office Hours: Mon. & Wed. 11:30-12:30 or by appointment |
| Web site: |
http://www.math.washington.edu/~lee/Courses/548 (or from the Math Department home page, follow the links Current Class Information -> Math 548) |
Books:
There will be no textbook for this course. Early in the quarter, I will hand out a list of suggested references that you can consult if you wish; these books will be placed on reserve in the Math Research Library.
Prerequisite:
Math 547 (Riemannian geometry). If you want to brush up on your basic Riemannian geometry, ask me for a copy of last quarter's Math 547 lecture notes, or download them here. Some acquaintance with homology theory and/or partial differential equations would be helpful, but I will not assume any prior knowledge of these subjects.
Homework and grades:
I will assign homework problems on an irregular basis. Your grade will be based on how many of these you do correctly: roughly speaking, getting 80% of the assigned problems correct will get you a 4.0, and 60% a 3.0.
If you have passed prelims, you may be exempted from turning in homework with my permission. If you wish to be exempted, please give me a written request, showing the following information:
The topic for this quarter is Bundles, connections, and characteristic classes. Here's a rough outline of the syllabus:
| Bundles: |
Vector bundles: definitions and examples Constructing new bundles from old Fiber bundles Structure groups Principal bundles and associated bundles Classifying spaces Examples: G-structures and spin structures | Connections: | Connections in vector bundles Connections in principal bundles Moving frame approach Curvature Flat bundles and representations of the fundamental group |
Characteristic Classes: | Chern classes Pontryagin classes The Chern/Weil construction The topological construction The Chern-Gauss-Bonnet Theorem |
Yang-Mills Theory: | The Yang-Mills equations Self-duality in 4-dimensional Riemannian geometry Instantons and monopoles |
Depending on time and how my interests and those of the audience develop, I might touch on one or more of the following topics: self-dual Einstein metrics on 4-manifolds; Donaldson invariants; Seiberg-Witten theory; Chern-Simons classes; or other topics.