Speaker: James Maynard
17 June, 2020 13:00 UTC
Abstract: Almost 80 years ago Duffin and Schaeffer conjectured a beautiful strengthening of Khinchin’s classical result: Given a sequence of possible forms of rational approximation, either almost all reals can be approximated in this manner or almost none can be, and there is a simple calculation to tell which case we are in. I’ll talk about recent work with D. Koukoulopoulos which establishes this conjecture. This relies on a blend of different techniques, recasting the problem as a structural question in additive combinatorics, and then approaching this via studying a particular family of graphs to reduce it to a problem in analytic number theory.