Terence Tao (UCLA): Pseudorandomness of the Liouville function

The Liouville pseudorandomness principle (a close cousin of the Mobius pseudorandomness principle) asserts that the Liouville function λ(n), which is the completely multiplicative function that equals −1 at every prime, should be "pseudorandom" in the sense that it behaves statistically like a random function taking values in −1,+1. Various formalizations of this principle include the Chowla conjecture, the Sarnak conjecture, the local uniformity conjecture, and the Riemann hypothesis. In this talk we survey some recent progress on some of these conjectures.