## István Gaál (University of Debrecen): Thue equations and monogenity of algebraic number fields

 Wednesday, 18. April 2018, 10:00 - 12:00
Abstract. An algebraic field K is monogene if its ring of integers is a simple ring extension of Z. In this case the powers of the generating element form an integral basis of K, called power integral basis.

It is a classical problem of algebraic number theory to decide if a number field is monogene and to determine all generators of its power integral bases. The problem can be reduced to the resolution of a certain type of diophantine equations called index form equations.

In some cases these index form equations are Thue equations or can be solved by using Thue equations (and its generalizations). Therefore we explain the basic methods of solving one of the most classical types of diophantine equations, the Thue equations.

Some recent results are on infinite parametric families of number fields and on the problem of monogenity and power integral bases in these families of fields.
Location : Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged