## Riemann surfaces and Integrable Systems

### Prof. Tamara Grava

Contents:

- Definition of Riemann surfaces, classification, uniformization theorem, Kleinian groups
- Functions and forms on Riemann surfaces. The Riemann-Roch theorem
- Hurwitz theorem, definitions and open problems
- Theta-functions and Jacobi varieties
- Application to Integrabe Systems: nonlinear integrable PDEs (periodic solutions)
- KP equation, NLS equation, KdV equation and spectral theory - small dispersion limit