##### Department of Mathematics,

University of California San Diego

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### Group Actions Seminar

## Brandon Seward

#### UC San Diego

## An introduction to the f-invariant

##### Abstract:

The f-invariant was introduced by Lewis Bowen in 2008 and is a real-valued isomorphism invariant that is defined for a large class of probability measure-preserving actions of finite-rank free groups. Most notably, the f-invariant provided the first classification up to isomorphism of Bernoulli shifts over finite-rank free groups. It is also quite useful for the study of finite state Markov chains with values indexed by a finite-rank free group. The f-invariant is conceptually similar to entropy, and it has a formal connection to sofic entropy. In this expository talk, I will introduce the f-invariant and discuss some of its basic properties.

### November 17, 2020

### 9:00 AM

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

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