Sophie Maclean

Pair correlations and the metric Poissonian property

This talk studies the distribution of dilated integer sequences modulo 1 i.e. the distribution of $\alpha\mathcal{A}$ mod $1$, where $\alpha\in[0,1)$ and $\mathcal{A}\subseteq\mathbb{N}$. Specifically, we look at when such sequences have a pseudorandom property. To do this, we will consider the equidistribution and the gap distributions of such sequences, looking at what has been proven, and what still remains a conjecture.