Integral points on moduli schemes and Thue equations

Abstract: We will explain a way how one can use moduli schemes and their natural forgetful maps in the study of certain classical Diophantine problems (e.g. finding all integral points on hyperbolic curves). To illustrate and motivate the strategy, we consider the case of cubic Thue equations and we discuss a joint project with Matschke in which we solved many cubic Thue equations.