This course is an introduction to modular forms, with an emphasis on their relationship to Galois representations.
Notes will be posted here throughout the course.
Enrolled students should attempt, at a minimum, the starred problems.
Errors can be reported in the same Google doc as above.
When available, the notes above are the best resource for the course. If you'd like the illegible and unintelligible notes that I wrote during the lecture (and often back-edited, for extra unintelligibility!), those can be found below.
6/24: A (non)introduction to modular forms (good notes above, bad notes here).
6/26: Galois representations, part 1 (notes).
6/29: p-adic numbers, valuations, and completions (presented by Savvy, notes).
7/01: Galois representations, part 2 (notes).
7/03: No class.
7/06: Galois representations, part 3 (notes).
7/08: Galois representations, part 4 (notes).
7/10: Galois representations, part 5 (notes).
7/13: Zeta function: analytic properties and functional equation (presented by Gaurav, notes).
7/15: Elliptic curves, part 1 (notes).
7/17: Elliptic curves, part 2 (notes).
7/20: The Weierstrass p-function (presented by CJ, notes).
7/22: Elliptic curves, part 3 (notes).
7/24: Elliptic curves, part 4 (notes).
7/27: Divisors on algebraic curves (presented by Alec, notes, annotated notes).
7/29: Modular curves, part 1 (notes).
7/31: Modular curves, part 2 (notes).
8/03: Modular curves, part 3 (notes).
8/05: Modular forms, part 1 (notes).
8/07: Modular forms, part 2 (notes).
8/10: Modular forms, part 3 (notes).
8/12: Modular forms, part 4 (notes).
8/14: Modular forms, part 5 (notes).
8/17: The Galois representation attached to an elliptic curve (notes).
8/19: The modularity theorem (notes).