Permission of the instructors. You will need a basic knowledge
of complex function theory at the level of Complex Analysis by
Lars Ahlfors or
Functions of One Complex Variable, Volume I, by
John Conway.
Outline
Riemann's analysis of finite genus one dimensional complex manifolds
is a mathematical gem. This course will be an introduction to these
manifolds. The topics are
Definitions and Examples
Topology of Riemann Surfaces
Differential Forms
Integration Formulae
Hodge Decomposition
Harmonic Differentials
Meromorphic Functions and Differentials
Compact Riemann Surfaces
Bilinear Relations
The Riemann--Roch Theorem
Hyperelliptic Riemann Surfaces
Torelli's Theorem
Additional topics as time permits
Automorphisms of Compact Riemann Surfaces
Theta Functions
Text
H. M. Farkas and I. Kra, Riemann Surfaces,
Springer-Verlag, 2nd Edition, 1992.
Other possible references include
A. Beardon, Riemann Surfaces - A Primer.
C. H. Clemens, A Scrapbook of Complex Curve Theory.
R. Miranda, Algebraic Curves and Riemann Surfaces.
G. Springer, Introduction to Riemann Surfaces.
All handouts, problem sets, etc. will be posted on the web
here.