E-mail: andras "at" math.stanford.edu
Tentative office hours: TBA
Class location: MWF 10-10:50am, McCullough 126.
Textbook: `The Atiyah-Patodi-Singer Index Theorem' by R. B. Melrose and volume 2 of Michael Taylor's `Partial differential equations', both recommended. Some of the lectures will be typed up as lecture notes.
A knowledge of microlocal analysis is NOT a pre-requisite. I will provide a quick overview of the background. For a more thorough background on this, please see Richard Melrose's lecture notes and volume 2 of Michael Taylor's PDE book.This is an advanced graduate PDE class, focusing on Melrose's so-called b-(pseudo)differential operators, but no PDE background is required. (Thus, 256A is not a prerequisite.) However, a thorough knowledge of functional analysis and Fourier analysis (as presented in the Math 205 sequence) is a must. In the Riemannian world b-analysis includes manifolds with cylindrical ends as well as asymptotically Euclidean spaces, and in the Lorentzian world such diverse spaces as Minkowski space, a neighborhood of the static patch of de Sitter space, and Kerr-de Sitter space, as well as various spaces which asymptotically have a similar (but not necessarily the same!) structure. In addition, b-analysis helps analyze the standard boundary value problems in wave propagation; time permitting this will be discussed as well. Students with a strong background can take 205B concurrently with 256B; this requires permission of the instructor.
Rough outline of the course (probably too optimistic):
Grading policy: There may be a couple of (short) problem sets which must be handed in, but due to unavailability of graders, will not be graded carefully.
The homework will be due either in class or by 9pm in the instructor's mailbox on the designated day. You are allowed to discuss the homework with others in the class, but you must write up your homework solution by yourself. Thus, you should understand the solution, and be able to reproduce it yourself.