Analysis Seminars
This seminar series is aimed at staff, postgraduates, and final year undergraduates at the University of St Andrews; anybody else who is interested in attending is welcome to join. The intention is to provide a background in analysis, with an emphasis on the research interests of the group.
The seminar takes place on Tuesday afternoons at 15:00 in Tutorial Room 1A of the Mathematics Institute. A historical list of seminars can be found here.
NB Simon Baker's seminar on the 10th of September will take place in Lecture Theatre C of the Mathematics Institute.
Spring 2025
September 10, 2025
Simon Baker:A seemingly innocuous generalisation of binary expansions involves replacing 2 with a parameter q satisfying 1 < q < 2. This change leads to substantially different behaviour. For instance, a Lebesgue typical point has uncountably many expansions in base q. Moreover, for any integer k, there exists q and x such that x has precisely k expansions in base q. This is contrary to the case of binary expansions where every point has a unique expansion apart from a countable set of exceptions with precisely two. In this talk I will discuss some recent results on those bases that admit points with precisely k expansions. This talk will be based upon joint work with George Bender.