Yoshikata Kida (IHÉS)

"Measure-theoretic rigidity for mapping class groups"

I present rigidity for mapping class groups of compact orientable surfaces in the sense of measure equivalence, which is a measure-theoretic counterpart of quasi-isometry in geometric group theory.

This rigidity makes it possible to describe a locally compact second countable group containing a lattice isomorphic to the mapping class group.

I also review rigidity results for lattices in simple Lie groups of higher rank, due to Zimmer and Furman.