Attention : Horaire et Salle inhabituels, de 11h à midi en salle 2P8

Résumé :  (A joint work with Tom Meyerovitch and Yuqing Frank Lin) Let G be a countable group, Ord(G) the (compact, metrizable) space of all the linear orders on G. The group naturally acts on this space from the left (there is also a right action, but we will ignore it in this talk). A left invariant order on G is a fixed point for this action, and the group itself is called left orderable if such a fixed point exists. An invariant random order (IRO) is a Borel, G-invariant probability measure on Ord(G). This notion, defined by Alpeev, Meyerovitch and Ryu, is more flexible for example since every countable group admits an IRO. In a joint work with Tom Meyerovitch and Yuqing (Frank) Lin. We study this notion and show it is not true that any partially defined order can be extended to an IRO. Later it was shown by Alpeev that the property "every partially defined random order is extendable to an IRO" is actually equivalent to the amenability of the group G.