Metrizable universal minimal flows of Polish groups have a comeagre   orbit
  We prove that, whenever $G$ is a Polish group with metrizable universal minimal flow $M(G)$, there exists a comeagre orbit in $M(G)$. It then follows that there exists an extremely amenable, closed, coprecompact $G^*$ of $G$ such that $M(G) = \hat{G/G^*}$. 
Ita\"i Ben Yaacov, Julien Melleray, Todor Tsankov
math.DS math.LO