Andrew Treglown

Some results on sums in the integers

A set of integers is sum-free if it contains no solutions to the equation x+y=z. A fundamental theorem of Schur from 1916 asserts that, provided n is sufficiently large, {1,...,n} cannot be partitioned into r sum-free sets. In the first part of the talk we consider bounds on Folkman's theorem, a wide generalisation of Schur's theorem. In the second half we switch emphasis and consider complexity questions for sum-free sets. This includes joint work with Kitty Meeks as well as Jozsi Balogh, Sean Eberhard, Bhargav Narayanan and Adam Wagner.