Techniques from Diophantine approximation have many applications
to Diophantine equations. For instance, the Thue-Siegel-Roth theorem can be used to prove that the so-called Thue equations have only finitely many solutions. However, the proof does not yield a bound on the size of solutions and is therefore ineffective. In this talk, we will discuss some applications of Roth's theorem and its higher-dimensional generalization to Diophantine equations.
