Description
Austrian-Hungarian Diophantine Number Theory seminar
Abstract: A finitely generated domain over ℤ is a domain containing ℤ generated by finitely many elements, i.e., ℤ[z1,...,zt] where z1,...,zt may be algebraic or transcendental. In the early 1960s, Lang proved several finiteness results for Diophantine equations with unknowns taken from a finitely generated domain as above, but his proofs are ineffective. In the 1980s, Gyõry developed an effective method to deal with Diophantine equations but this worked only for a restricted class of domains. Gyõry's method combines Baker's theory on linear forms in logarithms with effective methods for Diophantine equations over function fields and an effective specialization method. Some years ago, Gyõry and the speaker extended this to all finitely generated domains. Since then, this has been applied to several classes of Diophantine equations, in works of Gyõry and the speaker, Bérczes and Koymans. In his lecture at the recent workshop Gyõry gave a survey of these applications. In my talk I would like to explain in more detail the method, and also say something on recently developed techniques.
link: https://uni-salzburg.webex.com/uni-salzburg/j.php?MTID=m409f757947cd3eee89e5e52a553febe4