Riemann surfaces and Integrable Systems

Prof. Tamara Grava


  1. Integrable systems:
    • random NxN Hermitian matrices,
    • Toda lattice,
    • large N limit and continum limit of Toda lattice,
    • graphical enumeration.
  2. Riemann surfaces:
    • 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 Integrable Systems: nonlinear integrable PDEs (periodic solutions).
    • KP equation, NLS equation, KdV equation and spectral theory - small dispersion limit.