2015
Dec
08

# Dynamics & probability: Brandon Seward (HUJI): "Positive entropy actions of countable groups factor onto Bernoulli shifts"

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)

Title: Positive entropy actions of countable groups factor onto Bernoulli shifts

Abstract: I will prove that if a free ergodic action of a countable group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countable groups the well-known Sinai factor theorem from classical entropy theory. As an application, I will show that for a large

class of non-amenable groups, every positive entropy free ergodic action satisfies the measurable von Neumann conjecture.

Abstract: I will prove that if a free ergodic action of a countable group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countable groups the well-known Sinai factor theorem from classical entropy theory. As an application, I will show that for a large

class of non-amenable groups, every positive entropy free ergodic action satisfies the measurable von Neumann conjecture.