Diophantine Equations

The course will give an overview of the existing methods for investigating integer and rational solutions to Diophantine equations. It will include both the algebraic, analytic and model theory aspects of the subject. The course will take the format of three 6-hour mini-courses, supported by exercise classes.

1. Rational Points
A. Rational points on curves (Michael Stoll, Bremen)
B. Higher-dimensional varieties (Alexei Skorobogatov, Imperial)

2. Integral Points
A. Basic methods and solubility (Jennifer Park, McGill)
B. Analytic methods, (Trevor Wooley, Bristol)

3. Elliptic and modular curves
A. Elliptic curves (Tim Dokchitser, Bristol and Vladimir Dokchitser, Warwick)
B. Modularity (Andrew Granville, Montreal/UCL)