Simon Baker: Exceptional digit frequencies and expansions in non-integer bases

A beta expansion is a representation of a real number. Importantly this representation is often not unique. Consequently, one can ask whether amongst the set of representations does there exist one that satisfies a certain property. In this talk we examine this question in the context of digit frequencies. I will discuss some recent work where it is shown that as our base approaches 1, the set of realisable digit frequencies fills out the simplex.