Gowers' Ramsey Theorem with multiple operations and dynamics of the   homeomorphism group of the Lelek fan
  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. 
Dana Barto\v{s}ov\'a and Aleksandra Kwiatkowska
math.LO math.CO math.DS