##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Andrei Alpeev

#### Euler International Mathematical Institute

## Amenabilty and random orders

##### Abstract:

An invariant random order is a shift-invariant measure on the space of all orders on a group. It is easy to show that on an amenable group, any invariant random order could be invariantly extended to an invariant random total order. Recently, Glaner, Lin and Meyerovitch showed that this is no longer true for $\mathrm{SL}_3(\mathbb{Z})$. I will explain, how starting from their construction, one can show that this order extension property does not hold for non-amenable groups, and discuss an analog of this result for measure preserving equivalence relations.

Host: Brandon Seward

### October 6, 2022

### 10:00 AM

Zoom ID 967 4109 3409

(email an organizer for the password)

Research Areas

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