Fixed points on null and tame flows for groups of automorphisms

Using a generalization of the Kechris-Pestov-Todorčević correspondence due to Nguyen Van Thé we obtain fixed point theorems for null and tame actions of groups of the form Aut( F), where F is a Fraïssé structure. In particular we show that if Age( F) is a free joint embedding class, then every null flow Aut( F) X has a fixed point, while if Age( F) is a free amalgamation class, then every tame flow Aut( F) X has a fixed point.