| # |
Date |
Topic (references) |
Materials |
| 1 | 2/5 | Automorphisms of the upper half plane and hyperbolic geometry (Miyake 1.1-1.4) | notes, primer |
| 2 | 2/7 | Topological group actions and Fuchsian groups (Miyake 1.5, Voight 33-34) | notes |
| 3 | 2/12 | Fuchsian groups and Dirichlet domains (Miyake 1.6-1.7, Voight 36-37) | notes |
| 4 | 2/14 | Cusps and stabilizers of Fuchsian groups (Miyake 1.5,1.7-1.8, Voight 37) | notes |
| 5 | 2/20 | Lattices, arithmetic groups, and triangle groups (Takeuchi, Voight 38) | notes |
| 6 | 2/21 | Automorphic forms, Petersson inner product (Miyake 2.1) | notes |
| 7 | 2/26 | Meromorphic differentials (Miyake 2.2-2.3, Diamond-Shurman 3.3-3.4) | notes | |
| 8 | 2/28 | Dimension formulas (Miyake 2.3-2.5) | notes | |
| 9 | 3/11 | Poincaré and Eisenstein series (Miyake 2.6) | notes | |
| 10 | 3/13 | Hecke algebras (Miyake 2.7-2.8) | notes | |
| 11 | 3/19 | Modular forms for congruence subgroups (Miyake 4.3-4.5) | notes | |
| 12 | 3/20 | Hecke operators for congruence subgroups (Miyake 4.5) | notes | |
| 13 | 4/1 | The Riemann zeta function and the Mellin transform (Miyake 3.2) | notes |
| 14 | 4/3 | Modular form L-functions (Miyake 4.3) | notes |
| 15 | 4/10 | Newforms and twists (Miyake 4.3 and 4.6) | notes |
| 16 | 4/17 | The trace formula (Miyake 6.1) | notes |
| 17 | 4/22 | Traces of Hecke operators (Miyake 6.3-6.4) | notes |
| 18 | 4/24 | Modular Jacobians and modular abelian varieties (Diamond-Shurman 6.1-6.3) | notes |
| 19 | 4/24 | Modular curves and the j-function (18.783 Lectures 14-19) | notes |
| 20 | 5/2 | Galois representations attached to elliptic curves (18.783 Lecture 12, Serre) | notes |
| 21 | 5/2 | Level structure and modular curves XH (RSZB 2.2-2.3) | notes |
| 21 | 5/2 | Counting points on XH and decomposing JH (RSZB 5-6) | notes |
