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 |
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Spring
2021
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