* ASSIGNMENT 1*: PDF (Due March 11 in class)

ASSIGNMENT 2: PDF (Due April 17 in class)

ASSIGNMENT 3: PDF (Due May 15 in class)

OFFICE HOUR: Thursday 4:30-5:30pm (better to ask questions via email, this will usually produce better responses)

Instructor: Marco Gualtieri [] office 2-171

Topics: A mixture of nonlinear geometric analysis, algebraic geometry, and Riemannian geometry. Uniformization, Moduli space and Teichmuller space, Line bundles and divisors, Sheaves and cohomology, the Riemann-Roch theorem.

Main text: Jost's "Compact Riemann Surfaces", 3rd edition.

This is a challenging but original treatment of Riemann surface theory which provides a modern approach to the uniformization theorem as well as Teichmuller theory. To make up for a slight algebraic weakness (Sheaves), it should be supplemented by any of the texts below.

Backup texts:

- Farkas & Kra, "Riemann Surfaces", 2nd edition.
- Gunning, "Lectures on Riemann surfaces".
- Griffiths & Harris, "Principles of Algebraic Geometry".

Evaluation: 100% assignments (5 (no, actually 3) assignments, 20% (no, actually (100/3) % each.)