This is a graduate class in differential geometry.
This semester the subject is the index theorem for generalized Dirac operators and its proof via heat kernels. The syllabus can be found
here.
Time: T/Th 12:30 PM -- 1:45 PM.
Location: MCS B31
Course schedule and notes
In parentheses are the (approximate) sections of the textbook ``Heat kernels and Dirac operators'' by Berline, Getzler, and Vergne = BGV.
I am updating a terse summary of the main topics covered in lectures
here (last updated: 2/25).
January 23: Introduction to the course. Notes.
January 25: Overview of differential geometry. Notes.
January 30: Differential operators and generalized Laplacians. Notes.
February 1: Classification of generalized Laplacians. Notes.
February 6: Formal adjoints, density bundle. Notes.
February 8: Solution to heat equation on Euclidean space. Notes.
February 15: Schwarz kernels. Notes.
February 20: Existence of heat kernels, part I: iterative step. Notes.
February 22: Existence of heat kernels, pat II: formal heat kernels. Notes.