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.