18.156: Differential Analysis, Spring 2012

Richard Melrose

This is the home page for the course 18.156 at MIT for Spring 2012.

Recent changes:

• Another typo fixed in the problems, there may be more.
• Two (significant) typos fixed in the problems thanks to Jonathan.
• Lecture 6: Elliptic operators on compact manifolds are Fredholm. The Laplacian. Constructing a local parametrix.
• Problem set 1 is up.
• Lecture 2: Dirac/Clifford. Constant coefficient Dirac operators, Clifford algebra, spin representation (stated only). Outline of local elliptic regularity for elliptic operators with smooth coefficients -- reduced to 3 Lemmas.
• Lecture 1: Coordinate invariant definitions of cotangent space and differential of a smooth map etc. Reminder of local elliptic regularity for constant coefficient operators.
• 10 February, 2012: Finally I am setting up the web-page. It may take a little while.
• Old changes

Basic facts:

• Lectures: TR 11-12:30 in 2-146.
• Office hour: W 10-11 is a possibility, or by arrangement.
• Email to me at rbm AT math.mit.edu will likely be answered!
• Problem sets Cal
  Namely, Feb
• No exams or tests. Grades will be based on homework alone.
• Lecture notes
  I will add here a brief description of what I actually said as we go along this year, plus suggestions as to what to read before/after lectures.
  • Lecture 3
  • Lecture 4
• Syllabus May change a little with time but my best guess as to where I will go.