Riemann surfaces and Integrable Systems

Prof. Tamara Grava


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