Gap distributions and the Metric Poissonian Property 

When studying dilated arithmetic sequences, it is natural to wonder about their distribution. Whilst it is relatively achievable to ascertain whether the resulting sequence is equidistributed, is it much more difficult to say much about gap size between consecutive elements of the new set? In this talk I will explore the gap distributions in dilated arithmetic sequences modulo 1, including what it means for a sequence to have the metric poissonian property. I will also give an overview of the current progress and what I am aiming to discover in my own work.