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Integrable systems and Riemann surfaces

Course Type: 
PhD Course
Academic Year: 
50 h

Course material

  1. Riemann surfaces: definition and examples
  2. Holomorphic and meromorphic functions on Riemann surface
  3. Compact Riemann surface: genus, monodromy, homology
  4. Differentials on Riemann surface and Riemann bilinear relation
  5. Jacobi variety and Abel theorem Divisors and Riemann-Roch theorem
  6. Jacobi inversion problem and theta functions.
  7. Integrable systems: the Toda Lattice with periodic boundary conditions
  8. Integrable systems with random initial data and connection with the theory of random matrices and statistical mechanics.
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