Math 844, Elliptic Curves and Modular Forms - Fall 2013

Nigel Boston

Contact Information

303 Van Vleck Hall

Telephone: 263-4753.



Office Hours:Wednesdays 1:30-3:00 (in 3619 EH), Thursdays 9:30-11:00 (in 303 VV).


Useful Web Materials

Elliptic curves resources
Elliptic curve resources
Elliptic curve rank records
Rusin's elliptic curve links
Elkies' Computational Number Theory Page

Course Description

This course is an introduction to elliptic curves and arithmetic geometry. Elliptic curves play a central role in modern arithmetic geometry and even in applications to cryptography. On the elliptic curve side, we'll cover elliptic curves over finite fields, over the complex numbers, and over the rationals. We'll prove the Mordell-Weil theorem, discuss torsion, Tate-Shafarevich groups, elliptic curves with CM, and integer points on elliptic curves and Diophantine approximation. We'll discuss associated modular forms and L-functions and the notion of modularity of an elliptic curve. We'll discuss generalizations to other varieties, in particular curves and questions regarding their rational points. Applications and open problems will be mentioned throughout.


Homework 1, due Sep 20
Homework 2, due Sep 27
Homework 3, due Oct 4
Homework 4, due Oct 18
Homework 5, due Oct 25
Homework 6, due Nov 1
Homework 7, due Nov 8
Homework 8, due Nov 22
Homework 9, due Dec 6
Homework 10, due Dec 13