[McGill] [Math.Mcgill] [Back]

Clay Institute Summer School

The arithmetic of curves

From July 24 to August 4 I will be running a 15-hour mini-course on the arithmetic of curves.
This mini-course is part of the Clay Institute Summer School that is taking place in Gottingen, Germany, from July 17 to August 11, 2006.

The mini-course will be given in two parts, in two consecutive weeks, and the syllabus is roughly as follows.

Week 1: The key finiteness theorems (8 hours)

1. Overview
2. The Mordell-Weil theorem
3. Faltings' Theorem
4. Modular curves and Mazur's Theorem
5. Fermat curves and Wiles' Theorem

Week 2: Rational points on elliptic curves (7 hours)

1. Heegner points
2. The theorems of Gross-Zagier and Kolyvagin
3. Shimura curve parametrisations
4. p-adic uniformisation
5. Stark-Heegner points