• Smooth Operator Algebras and K-theory


    These are lecture notes from the course I taught at Berkeley, Fall 2008. Still being revised!
    Bkly08

  • Real Blow up


    Three lectures at MSRI, August 2008.
    InSisp

  • Lectures on pseudodifferential operators

    These are notes from a course in 2005 and are currently being revised (surprise!)
    Last modified, 29 November, 2006.
    • As postscript all (ps)
    • In acrobat format all (pdf)
      • Introduction/Chapter 1 (Compactifications of a vector space)
      • Chapter 2 (Conormal distributions at the origin)
      • Chapter 3 (Conormality at the zero section)
      • Chapter 4 (Conormality at a submanifold)
      • Chapter 5 (Pseudodifferential operators)
      • Chapter 6 (Ellipticity)
      • Chapter 7 (Localization and composition)
      • Chapter 8 (Smoothing operators)
      • Chapter 9 (Homotopy invariance of the index)
      • Chapter 10 (Chern forms and the Fredholm determinant)
      • Chapter 11 (Toeplitz operators)
      • Chapter 12 (Linearization of symbols)
      • Chapter 13 (Classifying sequence for K-theory)
      • Chapter 14 (Bott periodicity)
      • Chapter 15 (Fibrations and families)
      • Chapter 16 (Product-type symbols)
      • Chapter 17 (Product-type conormal distributions)
      • Chapter 18 (Product-type pseudodifferential operators)
      • Chapter 19 (Multiplicativity and excision)
      • Chapter 20 (Chern character)
      • Chapter 21 (Families Atiyah-Singer index theorem)
      • Chapter 22 (Eta forms)
      • Chapter 23 (Index for product-type families)
      • Chapter 24 (Index theorems and applications)

  • Introduction to Microlocal Analysis

    These notes are currently (Spring 2000) being extensively revised, new versions are gradually appearing at 18.157

    These notes are from a variety of courses starting (as you might guess) in 1990. Parts of this are in a parlous state, but if you are interested here the are:

    • June 12, 1998. First version of a new Chapter 6, on Elliptic Boundary Problems. Very preliminary
      Chapter6.dvi
      Chapter6.ps
      August 27, 1997 -- mainly cosmetic changes to the first 4 Chapters.
    • Whole thing as an `acrobat' file iml.pdf or as a postscript file iml90.ps or as a dvi file iml90.dvi (August 27, 1997)
    • Front and rear stuff :iml90e.ps or iml90e.dvi (August 27, 1997)
    • Chapter 1 (Tempered distributions and Fourier transform):iml90c1.ps or iml90c1.dvi (August 27, 1997)
    • Chapter 2 (Pseudodifferential operators) :iml90c2.ps or iml90c2.dvi (August 27, 1997)
    • Chapter 3 (Ellipticity and boundedness) :iml90c3.ps or iml90c3.dvi (August 27, 1997)
    • Chapter 4 (Wavefront set) :iml90c4.ps or iml90c4.dvi (August 27, 1997)
    • Chapter 5 (Manifolds) :iml90c5.ps or iml90c5.dvi (August 27, 1997)
    • Chapter 6 (The wave kernel) :iml90c6.ps or iml90c6.dvi (August 27, 1997)
    • Chapter 7 (K-theory) [Absent] :iml90c7.ps or iml90c7.dvi (August 27, 1997)
    • Chapter 8 (Hochschild homology) :iml90c8.ps or iml90c8.dvi (August 27, 1997)
    • Chapter 9 (The index formula) :iml90c9.ps or iml90c9.dvi (August 27, 1997)