Math 697B: Introduction to Riemann Surfaces
Fall 2010



Instructor: Paul Hacking, LGRT 1235H, hacking@math.umass.edu

Meetings:
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.

Course text: Introduction to algebraic curves, by Phillip Griffiths, AMS 1989. googlebooks.

Prerequisites: Math 421, Complex variables; Math 411-2, Introduction to Abstract Algebra I and II.

Homework:
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.)

Exams: There will be one midterm exam and one final exam. The midterm exam will be held in class on Thursday 10/28/10. The final exam will be a take home exam distributed on Friday 12/3/10 and due on Friday 12/10/10.
Midterm exam.
Final exam.

Grading: Your course grade will be computed as follows: Homework 30%, Midterm 30%, Final 40%.

Overview of course

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.




This page is maintained by Paul Hacking hacking@math.umass.edu