Doctoral School Mathematics and Scientific Computing

Abstract: Polynomial decomposition theory has a long history and dates back to the work of J.F. Ritt in the 1920s. Ritt studied the functional decomposition of a univariate polynomial over a field into prime (indecomposable) polynomials. Ritt's polynomial decomposition results have been applied in various wide-ranging contexts. In 2000, Bilu and Tichy succeeded in fully joining polynomial decomposition theory with the classical theorem of Siegel on finiteness of integral points of curves of genus greater than 0 to give a complete ineffective (no algorithm for determining solutions is given) finiteness criterion for the Diophantine equations of the form f(x)=g(y), where f(x) and g(x) are polynomials with rational coefficients. In this talk we give an overview of polynomial decomposition results often used in Diophantine equations settings and illustrate an application of Bilu-Tichy theorem. [hide abstract]