Aled Walker: An argument without quality: a short(er) proof of the Duffin—Schaeffer conjecture

Abstract:

In this talk I will discuss a novel proof of the Duffin—Schaeffer conjecture in metric diophantine approximation. Though heavily motivated by the ideas of Koukoulopoulos—Maynard’s breakthrough first argument, the new proof simplifies and strengthens several technical aspects. In particular, we avoid any direct handling of GCD graphs and their so-called ‘quality’. We also consider the metric quantitative theory of diophantine approximations, improving the error-term of Aistleitner—Borda—Hauke. This is based on joint work with Manuel Hauke and Santiago Vazquez Saez. No background in diophantine approximation or the Koukoulopoulos—Maynard method will be assumed. ​