# Seminars & Colloquia Calendar

Graduate Student Number Theory Learning Seminar

## Graduate Number Theory Seminar/ Learning Seminar

#### Chris Lutsko - Rutgers University

Location:  zoom
Date & time: Tuesday, 09 March 2021 at 4:00PM - 5:00PM

Abstract: It is not hard to determine when the sequence $$alpha n^{theta} mod 1$$ is uniformly distributed on the unit interval. I.e for fixed $$theta$$ we can find $$alpha$$ such that this sequence is uniformly distributed. Due, in part, to some connections to quantum chaos, many people have asked what can be said about the local statistics of such a sequence. In particular one can ask when does the sequence have the same local statistics as uniformly distributed random variables (Poisson statistics). In this talk, I’ll survey what is known about this question and then present a theorem (joint with Niclas Technau and in progress) about the pair correlation. The talk should be accessible to anyone with some background in harmonic analysis.

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