Materials of the Summer School on "Spectral Geometry," Göttingen 2014

Tutorial on pseudodifferential operators

• Part I: Motivation and definitions (by Magnus Goffeng)
• Part II: Algebraic and analytic properties (by René Schulz)

Daniel Grieser: Heat kernels on singular spaces

Basics of singular analysis

• Basics of the b-calculus
• Notes on polyhomogeneous functions
• Notes on real blow-up (by Richard Melrose)

Heat kernel construction

• Notes on the heat kernel

Elmar Schrohe: Heat trace expansions and Weyl's law on the asymptotics of eigenvalues

• Notes for the Summer School

Ingo Witt: Wave trace invariants

• Introduction to microlocal analysis
• Global aspects of Fourier integral operators