Santiago Dynamical Systems Seminar: “Independence of notions from dynamics: a descriptive set theoretic approach”

Abstract:

As a special case of a theorem of Pollington, the set of numbers that are normal in base 2, but not normal in base 3 is known to have full Hausdorff dimension. An interpretation of results such as this are that in some way the notions of normality in base 2 and normality in base 3 are “independent”.

The purpose of this talk is to introduce notions from descriptive set theory that may better capture this idea of independence: that of – and -completeness. For example, the previously mentioned set of numbers normal in base 2, but not normal in base 3 is known to be -complete by a recent result of Jackson, M., and Vandehey. Difference sets that satisfy these properties will also have additional interesting properties that will be discussed

Speaker: Bill Mance (Adam Mickiewicz University)
Venue: Room 2, Faculty of Mathematics, Pontificia Universidad Católica