Page 17 - 8th European Congress of Mathematics. 20–26 June 2021 • Portorož, Slovenia. Other Events Included in the 8ECM Programme.
P. 17
Open Panels and Society Meetings
ABSTRACT
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! I’ll talk about this problem and recent joint work with
Dimitris Koukoulopoulos which classifies when these options occur,
answering an old question of Duffin and Schaeffer. This relies on a fun
blend of different ideas, including ergodic theory, analytic number theory
and graph theory.
13
ABSTRACT
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! I’ll talk about this problem and recent joint work with
Dimitris Koukoulopoulos which classifies when these options occur,
answering an old question of Duffin and Schaeffer. This relies on a fun
blend of different ideas, including ergodic theory, analytic number theory
and graph theory.
13
