Short Talk: Antoine Poulin

When can a sample of an invariant random process on a directed tree G can be transformed to a sample of an invariant random process on a different tree H, with the further requirement that two samples are the same up to a graph automorphism of G if and only if the same is true for the resulting samples on H? When such processes exists, we say the trees G,H are measure equivalent. In this talk, we survey measure equivalence and give new results in the classification of trees.