Gowers' Ramsey Theorem with multiple operations and dynamics of the homeomorphism group of the Lelek fan
arXiv:1411.5134
Abstract
We generalize the finite version of Gowers' Ramsey theorem to multiple tetris-like operations and apply it to show that a group of homeomorphisms that preserve a "typical" linear order of branches of the Lelek fan, a compact connected metric space with many symmetries, is extremely amenable.
accepted to Journal of Combinatorial Theory, Series A