Text: Riemann surfaces by Simon Donaldson,
Lecture notes: I have writen notes based on Donaldson's book, they will be updated as the quarter progresses. As you probably expect, they may be full of typos and errors.
Here are the Lecture notes (updated 5-3 these probably won't be updated again this quarter, but I will post the notes I lecture from on Canvas)
Prerequisites: 210 A (and probably B)
Office hours: Wednesday after class and by appointment. Let me if you want to meet.
Other useful knowledge: Basic knowledge of covering spaces and fundamental groups (something you might see in 205A).
Some good places to look for background:
Low dimensional Geometry (from Euclidean surfaces to hyperbolic knots) by Francis Bonahon
Algebraic Topology by Hatcher
The course will have approximately 5 homework assignments and a final exam. Homework will be due regularly and late homework will be accepted with a penalty (the point of the homework is to keep you actively engaged with the material). I highly suggest that you read the homework assignments when they are assigned and think about them as lecture progesses through the material.
Grading break down:
homework: 50%
final: 50%
Homework 1 due Monday April 11: Problems 1-5 in the exercises of Section 1 of lecture notes.
Homework 2 due Monday April 25: Problems 1-5 in the exercises of Section 2 of the lecture notes.
Homework 3 due Wednesday May 11: Problems 1-4 and 5 or 6 in the exercises of Section 3 of the lecture notes.
Homework 4 due Monday May 23: Problems 1-5 in the exercises of Section 4 of the lecture notes
Homework 5 due Friday June 10, I highly suggest you finish it before this date. See HERE
Rough schedule:
Section 1 of lecture notes (roughly Chapter 3 of Donaldson and some background) 3 lectures.
Section 2 of lecture notes (roughly Chapter 4 of Donaldson and some background) 3 lectures .
Section 3 of lecture notes (roughly Chapter 5) 3-4 lectures.
Section 4 of lecture notes (chapters 8&9 and part of 10 of Donaldson)
Section 5 of lecture notes (aspects of chapter 12 of Donaldson)