##### Department of Mathematics,

University of California San Diego

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### Math 211 - Group Actions Seminar

## Matthieu Joseph - Graduate student

#### Ecole Normale Superieure de Lyon

## Rigidity and flexibility phenomenons in isometric orbit equivalence

##### Abstract:

In an ongoing work, we introduce the notion of isometric orbit equivalence for probability measure preserving actions of marked groups. This notion asks the Schreier graphings defined by the actions of the marked groups to be isomorphic. In the first part of the talk, we will prove that pmp actions of a marked group whose Cayley graph has a discrete automorphisms group are rigid up to isometric orbit equivalence. In a second time, we will explain how to construct pmp actions of the free group that are isometric orbit equivalent but not conjugate.

Host: Brandon Seward

### February 2, 2021

### 9:00 AM

### Zoom ID 967 4109 3409 (email Brandon Seward or Nattalie Tamam for the password)

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