M392C: Atiyah-Singer Index Theorem
Basic Information
Professor: Dan Freed, RLM 9.162
Office Hours: Mondays 3:00 - 4:30,
Wednesdays 2:00 - 3:00
For more details, see the First Day Handout
Projects
On Pseudodifferential Operators (Magdalena
Czubak)
Characteristic Classes (Haydar Oguz Erdin)
Anomalies and the Atiyah-Singer Index Theorem (Raphael Flauger)
Clifford algebra basics (Mike Gagliardo)
A fiexed point theorem for elliptic complexes (Alexander Kahle)
Lefschetz fixed point formula for elliptic complexes (Kevin Klonoff)
K-Theory, Periodicity, and a Simple Application (Parker E. Lowrey)
The soul theorem (Craig Michoski)
Index theorems and Morse Theory (Vivek Narayan)
Instantons and Self-Dual Gauge Fields (Jeffrey D. Olson)
On Witten's proof of the positive energy theorem
(Michael Ortiz)
A gerbe formulation of the Atiyah-Singer index
theorem (Phillip Schmitz)
The Atiyah-Bott formulation of the Lefschetz theorem
(Spencer Stirling)
Pseudodifferential Operators (Andrea Young)
Readings
Clifford modules (Atiyah, Bott, Shapiro)
Index of Elliptic Operators III (Atiyah, Singer)
See section 6 for a discussion of the signature operator.
On determinant line bundles (Freed)
Notes
These are notes I wrote more than 15 years ago. They were intended to become
a book... You may find them useful, though I warn you that there are errors
and some of the notation and points of view are different from the current
course.
Section 1 (Introduction)
Section 2 (Dirac Operators)
Section 3 (Ellipticity)
Section 4 (Heat Kernel)
Section 5 (Index Theorem)
Appendix (Exponential Coordinates)
Bibliography
Homework
Homework #1
Homework #2
Homework #3
Homework #4
Homework #5
Homework #6
Homework #7
Homework #8
Homework #9
Homework #10
Homework #11
Homework #12
Homework #13