Description: The main topic will be complex Riemann surfaces. Riemann surfaces are at the crossroads of complex analysis, algebraic topology, differential geometry, and algebraic geometry. This course will introduce them using the techniques of complex function theory, but we will develop the geometric and topological aspects as well. We will not assume any prior background in topology or geometry; anything we need will be developed as we go along.
Prerequisites: A semester course in complex analysis
Assessment: Weekly problem sets (40%): Due each Monday, except for the first set which is due September 6. They should be turned in during class. Homework assignments are not pledged. You are strongly encouraged to work together, though each student should write up her/his own submission.
Midterm exam (20%): A closed-book 80-minute take-home test, to be taken sometime between Friday, September 29 and Monday, October 2.
Final exam (40%): A closed-book three-hour take-home exam.
Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All discussions will remain confidential. Students with disabilities will need to also contact Disability Support Services in the Ley Student Center.
Office: Herman Brown 402
Phone: (713) 348-5261