Matt Palmer

Progress towards the Duffin-Schaeffer conjecture in number fields

Classical Diophantine approximation asks and answers questions about the density of the rational numbers in the real numbers. One of the main problems in this subject is the Duffin-Schaeffer conjecture; there have been increasingly general partial results towards this since its statement in 1941, but the full conjecture itself is still open.

The questions posed in classical Diophantine approximation can also be generalised to other settings. One of these possible generalisations is to replace the rational numbers by a generic number field K, and use K to approximate the various completions of K. In this talk, I will discuss partial results towards analogues of the Duffin-Schaeffer conjecture in number fields.