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.
Autumn 2022
September 20, 2022
Jonathan Fraser:The Fourier dimension of a measure captures the rate at which its Fourier transform decays at infinity. The Hausdorff dimension of a set, on the other hand, describes how the set fills up space on small scales by studying the cost of efficient covers. Despite how different they appear at first sight, these notions are intimately connected. Following the philosophy of 'dimension interpolation', I will introduce and discuss the 'Fourier dimension spectrum', which interpolates between the two notions. Time permitting, we will encounter applications to distance sets and sumsets.
September 27, 2022
Mike Todd:I’ll give an introduction to (exponential) decay of correlations in dynamical systems, how this can be proved and the relevant constants involved. Moving to symbolic dynamics gives a clearer perspective on the constants involved here: I’ll discuss where they come from and how they might be improved.
October 4, 2022
István Kolossváry: TBDOctober 11, 2022
Aleksi Pyörälä:During recent years, the prevalence of normal numbers in natural subsets of the reals has been an active research topic in fractal geometry. The general idea is that in the absence of any special arithmetic structure, almost all numbers in a given set should be normal, in every base. In our recent joint work with Balázs Bárány, Antti Käenmäki and Meng Wu we verify this for all self-conformal sets on the line. The result is a corollary of a uniform scaling property of self-conformal measures: roughly speaking, a measure is said to be uniformly scaling if the sequence of successive magnifications of the measure equidistributes, at almost every point, for a common distribution supported on the space of measures. Dynamical properties of these distributions often give information on the geometry of the uniformly scaling measure.