Logic Seminar

Julien MellerayUniversity of Lyon
A dynamical proof of a theorem of Giordano, Putnam and Skau

Friday, April 2, 2021 - 3:00pm
Zoom

A well-known theorem of Giordano-Putnam-Skau asserts that if $g, h$ are two minimal (= all orbits are dense) homeomorphisms of the Cantor space, which have the same sets of invariant Borel probability measures, then there exists a homeomorphism of the Cantor space which maps $g$-orbits onto $h$-orbits. I will try to explain the context of this result, and then present a new proof which is based on manipulations of Kakutani--Rokhlin partitions as well as a theorem of Krieger concerning minimal actions of some locally finite groups on the Cantor space. No prior knowledge of Cantor dynamics will be assumed.
This is joint work with Simon Robert (Lyon).