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MAI0101
Complex Functions and Riemann Surfaces/
Komplexa funktioner och Riemann-ytor

Number of credits: 8 hp

Examiner: Lars Alexandersson

Course literature: Jones and Singerman: Complex functions. An algebraic and geometric viewpoint, Cambridge University Press, ISBN 0 521 31366 X.

Course contents:

  • The Riemann sphere and its meromorphic functions.
  • Periodic meromorphic functions in the complex plane, in particular elliptic functions (doubly periodic functions)
  • The torus and its meromorphic functions.
  • Analytic and meromorphic continuation, the monodromy theorem and the fundamental group.
  • The Riemann surfaces of log z, z1/n and p(z)1/2, where p(z) is a polynomial.
  • Abstract Riemann surfaces.
  • The Riemann surface of an algebraic function.

Organization: TBA

Examination: TBA

Prerequisites: TATA60 Complex Analysis or equivalent. TATA34 Analysis honors course or TATM85 Functional analysis is recommended.


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Last updated: 2015-02-09