I am hoping that most of the lectures will be accessible to graduate students. I will cover as much of the following outline as time permits.
Periodic Schrödinger Operators
- brief physical motivation for studying periodic
Schrödinger Operators
- the idea of the Bloch decomposition
- outline of how to make the Bloch decomposition rigorous
- a nontrivial example - the Lamé Equation
Fermi Surfaces for Space Dimension d=2
- the free Fermi surface as a one complex dimensional curve in
two complex dimensions
- the effect of turning on interactions.
Review of Finite Genus Riemann Surfaces
Infinite Genus Riemann Surfaces
- a set of axioms
- Theta functions
- Zeros of the Theta Function and Riemann's Vanishing Theorem
- the Torelli Theorem