||8 credit points
||Evertse, J.H. (Universiteit Leiden), Beukers, F. (Universiteit Utrecht)
||Diophantine equations is the branch of number theory which studies solutions of polynomial equations in several unknowns in the ring of integers, rational numbers or in a given finite extension. Of course the most famous one is Fermat's equation x^n+y^n=z^n in integers x,y,z. In these lectures we give an overview of some of the main results and an insight in some of the techniques used. In the
study of diophantine equations one uses a large variety of techniques from algebraic number theory, p-adic numbers and algebraic curves.
The course will contain several very brief introductions into these subjects, so as to understand how they are used in diophantine equations. The discussion of diophantine equations themselves will then be based on two fundamental theorems by A.Thue and W.M.Schmidt. These theorems have a large number of applications in the area of diophantine equations.
||The format of every session is two hours of lecture followed by a one hour exercise class.
||Home work problems and oral examination.
||Literature: course notes to be handed out during the lectures.
||More course information.