In 2016, Tao formulated a conjecture on the Gowers uniformity of the Möbius function in short intervals, which he showed to be equivalent to both the (logarithmic) Chowla and Sarnak conjectures. I will discuss work where we prove this conjecture for intervals of length X𝜺. I will then discuss applications to superpolynomial word complexity for the Liouville sequence and to a new averaged version of Chowla’s conjecture.
This is joint work with Kaisa Matomäki, Maksym Radziwiłł, Terence Tao and Tamar Ziegler.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
