Title: Sequences modulo one - from uniform distribution to small scale statistics

Abstract: The theory of uniform distribution modulo one, which dates back to the pioneering work of Hermann Weyl in the beginning of the 20th century, deals with the distribution of fractional parts of real sequences in the unit interval. While the classical theory can be applied to various number theoretical problems, it focuses on the distribution of points in fixed intervals, which has a limited ability to characterize randomness (or rather, pseudo-randomness) of sequences. It is therefore better to study smaller scale statistics, namely, the distribution of points in small ("shrinking") intervals, in order to identify randomness. A natural scale to consider is the scale of the average gap ("the local regime"), which gives rise to interesting statistics such as the pair correlation and the gap distribution.

We will discuss results in this regime for several examples, including joint works with C. Aistleitner, S. Baker, S. Chaubey, and N. Technau.

Zoom: https://huji.zoom.us/j/84202575300?pwd=QXBvNjV0bDBWUmwxVkFIYXpzQ29RQT09