Pre-Conference Lecture Notes

Pre-Conference Lecture notes from Steve Zelditch (pdf format, click on title). These notes include preliminary material,  material to be covered during the lectures, and supplementary lectures. Students are strongly encouraged to familiarize themselves with this material before the conference. Note that the final format of the CBMS lectures may differ from the notes posted here.

Supplementary Materials

1.. Survey paper on Local and Global Analysis of Eigenfunctions on Riemannian Manifolds
2. Method of Stationary Phase

Lecture Notes for CBMS

 0.  Overview
 1.  Wave kernels and propagators on constant curvature spaces
 2.  Homogeneous distributions and generalized functions
 3.  Hadamard-Riesz parametrices for wave kernels (updated)
Symplectic Geometric Notions
 5.  Hamilton-Jacobi Theory
 6. Lagrangian Distributions and FIO's, I
 7. Lagrangian Distributions and FIO's, II. Symbols
 8. Lagrangian Distributions and FIO's, III. Symbol Composition
 9. Semiclassical Oscillatory Integral Operators
10. Phenomenology of Eigenfunctions
11. Estimates on Eigenfunctions
12.  Eigenfunctions and Nodal Sets 
13. Eigenvalues and Eigenfunctions on Compact Surfaces of Constant Curvature
14. Boundary Values of Eigenfunctions on Hyperbolic Surfaces
15. Quantum Ergodicity
16. Quantum Ergodic Restriction Theorems
17. Weak-* Limit Problem
18. Lower Bounds on Hypersurface Area of Nodal Sets 
19. Random Wave Models
20.. Local Weyl Laws 
21. Quantum Integrable Systems
22. Lp Norms of Eigenfunctions (joint with Chris Sogge and John Toth)
23. Spectral Rigidity of the Ellipse (joint with Hamid Hezari)


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