Prof. Claude LeBrun.
Office: Math Tower 3-108.
Office hours: TuTh 2:00--3:30, or by appointment.
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.
Oxford University Press, 2011.
Grades will be based on homework and class participation.
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