Title: Ergodicity of the Liouville system implies the Chowla conjecture
Abstract: The Liouville function assigns the value one to integers with an even number of prime factors and minus one elsewhere.
Its importance stems from the fact that several well known conjectures in number theory can be rephrased as conjectural properties
of the Liouville function. A conjecture of Chowla states that the signs of the Liouville function are distributed randomly on the integers,
that is, they form a normal sequence of plus and minus ones. Reinterpreted in the language of ergodic theory this conjecture asserts
that a system naturally arising from the Liouville function is a Bernoulli system. The main objective of this talk is to prove that the weakest
randomness property of this ``Liouville system'', namely ergodicity, implies Bernoullicity, and as a consequence the Chowla conjecture.