##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Julien Melleray

#### Université Lyon 1

## From invariant measures to orbit equivalence, via locally finite groups

##### Abstract:

A famous theorem of Giordano, Putnam and Skau (1995) states that two minimal homeomorphisms of a Cantor space X are orbit equivalent (i.e, the equivalence relations induced by the two associated actions are isomorphic) as soon as they have the same invariant Borel probability measures. I will explain a new "elementary" approach to prove this theorem, based on a strengthening of a result of Krieger (1980). I will not assume prior familiarity with Cantor dynamics. This is joint work with S. Robert (Lyon).

Host: Brandon Seward

### February 3, 2022

### 12:00 PM

Zoom ID: 967 4109 3409

Email an organizer for the password

Research Areas

Ergodic Theory and Dynamical Systems****************************