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Automatic sequences give rise to one of the basic models of computation and have remarkable links to many areas of mathematics, including dynamics, algebra and logic. Distribution of these sequences has long been studied. During the talk we will explore this topic from the point of view of higher order Fourier analysis.
As it turns out, many of the classical automatic sequences are highly Gowers uniform, while others can be expressed as the sum of a structured component and a uniform component much more efficiently than guaranteed by the arithmetic regularity lemma. We investigate the extent to which this phenomenon extends to general automatic sequences and consider some closely related problems that make sense for sparse sequences.
The talk is partially based on joint work with J. Byszewski and with C. Müllner.