Fall 2010

Classes: Tuesdays and Thursdays, 9:30AM - 10:45AM in LGRT 1114.

Review session: Thursday 4:15PM in LGRT 1234.

Office hours: Mondays 4-5PM and Wednesdays 4:15PM-5:15PM in LGRT 1235H.

HW1. Due 9/21/10.

HW2. Due 9/28/10.

HW3. Due 10/5/10.

HW4. Due 10/14/10.

HW5. Due 10/26/10.

HW6. Due 11/16/10.

HW7. (will not be graded.)

Midterm exam.

Final exam.

A Riemann surface is a geometric object glued from open subsets of the complex plane using holomorphic maps. They are of fundamental importance throughout geometry, analysis, and algebra. For example, it is a remarkable fact that every Riemann surface can be described as a complex algebraic curve, that is, the locus of zeroes of a polynomial in two complex variables. We will develop the theory of Riemann surfaces from the analytic perspective, following the text by Griffiths. Highlights will include the Riemann Roch theorem, which allows us to describe compact Riemann surfaces of low genus (number of holes) explicitly, and the relation of a Riemann surface to a "linear" geometric object called its Jacobian.