16th December 2019

University of Bristol

We are very pleased to welcome James Maynard to the University of Bristol for a Heilbronn colloquium.

James is primarily interested in classical number theory, in particular the distribution of prime numbers. His research focuses on using tools from analytic number theory, particularly sieve methods, to study primes.

**Title: **Approximating reals by fractions

**Abstract:** How well can you approximate real numbers by fractions 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.

The colloquium will take place in Lecture theatre 2.41, Fry Building at 16:00- 17:00 on Monday 16th December followed by a wine reception in the Fry Common room. To help us plan catering, please complete the short registration form if you are planning to attend the colloquium.