Gowers Norms of the Thue-Morse and Other Automatic Sequences

The Thue-Morse sequence is perhaps the simplest example of an automatic sequence. Various pseudorandomness properties of this sequence have long been studied. During the talk, I will discuss a new result in this direction, asserting that the Gowers uniformity norms of the Thue-Morse sequence are small in a quantitative sense. Similar results hold for the Rudin-Shapiro sequence, as well as for a much wider class of automatic sequences which will be introduced during the talk.

The talk is partially based on joint work with Jakub Byszewski.