| LEC # | TOPICS | KEY DATES |
|---|---|---|
1 | Introduction to Elliptic Curves | Problem Set 1 out |
2 | The Group Law and Weierstrass and Edwards Equations | |
3 | Finite Field Arithmetic | Problem Set 1 due Problem Set 2 out |
4 | Isogenies | |
5 | Isogeny Kernels and Division Polynomials | Problem Set 2 due Problem Set 3 out |
6 | Endomorphism Rings | |
7 | Hasse's Theorem and Point Counting | Problem Set 3 due Problem Set 4 out |
8 | Schoof's Algorithm | |
9 | Generic Algorithms for the Discrete Logarithm Problem | Problem Set 4 due Problem Set 5 out |
10 | Index Calculus, Smooth Numbers, and Factoring Integers | Problem Set 5 due |
11 | Elliptic Curve Primality Proving (ECPP) | Problem Set 6 out |
12 | Endomorphism Algebras | Problem Set 6 due |
13 | Ordinary and Supersingular Curves | Problem Set 7 out |
14 | Elliptic Curves over C (Part I) | Problem Set 7 due |
15 | Elliptic Curves over C (Part II) | Problem Set 8 out |
16 | Complex Multiplication (CM) | |
17 | The CM Torsor | Problem Set 8 due Problem Set 9 out |
18 | Riemann Surfaces and Modular Curves | |
19 | The Modular Equation | Problem Set 9 due Problem Set 10 out |
20 | The Hilbert Class Polynomial | |
21 | Ring Class Fields and the CM Method | Problem Set 10 due Problem Set 11 out |
22 | Isogeny Volcanoes | |
23 | The Weil Pairing | Problem Set 11 due Problem Set 12 out |
24 | Modular Forms and L-Functions | |
25 | Fermat's Last Theorem | Problem Set 12 due |