- What are the Garding inequalities? What are the statements for a symbol in class S? How do they change if the symbol is in class S_delta for some delta? (Zworski)
- What is Schnirelmann's theorem? Does the density one subsequence you extract depend on the operator? How does this apply to eigenvalues of the Laplacian on a compact manifold? (Zworski)
- What is the stable-unstable manifold theorem? How is it used in the WKB construction? Why can't you solve the eikonal equation using the method of characteristics in this case? (Zworski)