Liam Orovec, Department of Pure Mathematics, University of Waterloo
"Unique Representations of Real Numbers in Non-Integer Bases"
an infinite number of expansions for any given real number under any given base. We look at finding,
given a fixed positive real number x, the smallest base qs(x) for which x has a unique qs(x)-expansion.
Beginning with x = 1 we find the ever present Thue-Morse sequence will be helpful throughout the
talk. Having found our constant qKL = qs(1), the Komornik-Loreti constant, we will explore when
qs(x) < qKL. The majority of this talk will follow the Results due to Derong Kong which covers
the case where are expansions have only digits 0 and 1, in what time that remains we will look at
generalizing these results for larger alphabets.