Riemann Surfaces, Spring 2026
Latest Updates
- (May 5) Recorded lectures and lecture notes for this week are uploaded below. We will not meet on May 9. We will meet via Zoom on May 12.
- (April 27) Zoom meeting ID for lectures on May 12 and May 26: 830 1023 3847 (passcode: 736306)
- (April 25) HW3 is available (due May 19).
- (April 21) Please ensure your final presentation topic is discussed with me no later than April 30. We will use our class time on April 28 to go over your ideas; ideally, you should have your topic finalized by then.
- (April 21) The lectures on May 12 and May 26 will be held via Zoom. The meeting links will be posted on this course website.
- (April 21) We will not meet during the week of May 4–10. In lieu of our scheduled lecture on Saturday, May 9, a recorded lecture will be uploaded to this course website by the end of that day.
- (April 13) An additional choice of topic for final presentations was added.
- (April 3) Instructions and a list of possible topics for final presentations can be found below. The list of topics may be updated to include additional options.
- (April 1) HW2 is available (due April 21).
- (March 16) HW1 is available (due March 31).
Basic Course Information
- Instructor: Yu-Wei Fan
- Schedule: Tuesdays, 09:55-12:20 (we take only one 10-minutes break)
- Location: SIMIS Room 1010
- Grading Policy: Homework (40%) and Final Presentation (60%)
- Prerequisites: Basic complex analysis, topology, and algebra. All necessary tools will be developed when needed.
References
- Forster, Lectures on Riemann Surfaces
- Farkas-Kra, Riemann Surfaces
- Donaldson, Riemann Surfaces
Lecture Notes
Handwritten notes will be made available after each lecture.
- Lecture 1 (March 3): Definition of Riemann surfaces, basic examples
- Lecture 2 (March 10): Holomorphic maps between Riemann surfaces
- Lecture 3 (March 17): Covering maps, fundamental groups
- Lecture 4 (March 24): Universal cover, quotients of Riemann surfaces
- Lecture 5 (March 31): Differential forms
- Lecture 6 (April 7): Dolbeault cohomology
- Lecture 7 (April 14): Solving the Poisson equation
- Lecture 8 (April 21): Hodge decomposition theorem, uniformization theorem
- Lecture 9 (April 28): Cech cohomology
- Lecture 10 (May 9, special date; will have recorded lecture): Elliptic functions, modular forms
(Recording:
1,
2)
- Lecture 11 (May 12, via Zoom)
- Lecture 12 (May 19)
- Lecture 13 (May 26, via Zoom)
- Lecture 14 (June 2)
- Lecture 15 (June 9): Final Presentations
- Lecture 16 (June 16): Final Presentations
Homework Assignments
Students will complete a total of four homework assignments throughout the semester.
- HW1 (Due March 31 at 9:55am)
- HW2 (Due April 21 at 9:55am)
- HW3 (Due May 19 at 9:55am)
- HW4 (Due June 9 at 9:55am)
Final Presentation
During Weeks 15 and 16, students seeking a grade for this course will deliver a final presentation. We will discuss specific topics and time limits as the semester progresses.