**Fields of research**

Thue equations

Inhomogeneous Thue equations

Relative Thue equations

Infinite parametric families of parametric Thue equations

Norm form equations

Inhomogeneous norm form equations

Discriminant form equations

Index form equations

Power integral bases in algebraic number fields

Relative index form equations

Relative power integral bases in algebraic number fields

Constructive methods for the complete resolution of diophantine equations

Diophantine equations over global function fields

Infinite parametric families of algebraic number fields

Elements of minimal index