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Riemann Surfaces and Integrable Systems

Lecturer: 
Course Type: 
PhD Course
Academic Year: 
2020-2021
Period: 
February-March
Duration: 
40 h
Description: 

The main references shall be the course notes.

Prerequisite: complex analysis.

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 integration:
    - Riemann bilinear relation;
    - Jacobi variety and Abel theorem;
    - Divisors and Riemann-Roch theorem;
  5. Jacobi inversion problem and theta functions.
Exam: You need to solve an exercise and give a seminar on an agreed topic.
 
Starting period: February
 
Additional Material: 
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