James Maynard (Oct 23 - 2020, hosted by ICMS and University of Edinburgh)

Title: Approximating real numbers by fractions

How well can you approximate real numbers by rationals with denominators coming from a given set? Although this old question has applications in many areas, in general this question seems impossibly hard - we don’t even know whether e+pi is rational or not! If you allow for a tiny number of bad exceptions, then a beautiful dichotomy occurs - either almost everything can be approximated or almost nothing! James talks about this problem and presents an approach that relies on a fun blend of different ideas, including ergodic theory, analytic number theory and graph theory.