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