OS Reelle Geometrie und Algebra: Diophantine equations and polynomial decomposition
Friday, 08. February 2019
13:30 – 14:30
This event is part of an event series „Oberseminar Reelle Geometrie und Algebra“.
In my talk I will give an overview of my research in the field of Diophantine equations. Of my particular interest are Diophantine equations of separated variables type, $f(x)=g(y)$ in polynomials $f$ and $g$, and some related problems about the factorization of polynomials with respect to functional composition. I will then focus on the case of lacunary polynomials (polynomials with a bounded number of terms) and separated variables equations with lacunary polynomials. Finally, I will discuss some related Diophantine problems, such as the classical Diophantine equation asking for integers with all digits equal to one with respect to two distinct bases, and present some recent results of mine obtained jointly with Bennett and Gherga.