MAT 543 
Complex Analysis II 
Fall 2014 
TuTh 11:30--12:50
Math Tower 4-130

Prof. Claude LeBrun.
Office: Math Tower 3-108.
Office hours: TuTh 2:00--3:30, or by appointment.

Complex Analysis II: Riemann Surfaces

This course will offer a gentle introduction to the theory of Riemann surfaces, a rich and beautiful subject located at the crossroads between various mathematical disciplines, including complex analysis, algebraic geometry, Riemannian geometry, geometric topology, and partial differential equations. While the subject has a long and venerable history rooted in the classical theory of functions of a complex variable, our approach will be a modern one, aimed at introducing the student to the tools needed to study higher-dimensional complex manifolds. Topics will include: divisors, line bundles, sheaf cohomology, Dolbeault cohomology, Serre duality, projective embeddings, conformal geometry, uniformization, and the classification of Riemann surfaces of low genus.

While the lectures will be relatively self-contained, they will certainly presuppose a broad, basic mathematical knowledge on the level of the core courses. Students who have not yet passed the departmental comprehensive exam may therefore enroll only by permission of the instructor.

Homework #2

Recommended Textbook:
Simon Donaldson,
Riemann Surfaces,
First edition,
Oxford University Press, 2011.

Grades will be based on homework and class participation.

The Professor may be reached via e-mail by .
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