One Day Shrinking Targets Meeting: 24 Jan 2024

One Day Shrinking Targets Meeting: 24 Jan 2024

On Wednesday 24 January, we will have a one day meeting on shrinking targets at the University of Oulu. We will have three speakers:

and the event will be broadcast on Zoom as part of a One World Fractals Meeting.

Schedule Overview

The talks will be held in the afternoon, with a tentative schedule from 14:00—17:00, to allow time for participants to arrive. All talks will be held at the Linnanmaa campus of the University of Oulu, with exact room details to be determined. We will go for dinner after the talks.

Registration

There is no registration fee, but please register on the Registration Page (even if you are a local) to gauge attendance numbers. If you are only intending to attend the talks online, they will be streamed as part of a One World Fractals Meeting. You can register on oneworldfractals.org to be part of the mailing list.

Detailed Schedule

Location and Timing

The talks will be held on 24 January from 14:00 (GMT+2) until 17:15 in Room IT115.

  • 14:00 – 14:40: Xintian Zhang
  • 14:40 – 15:00: Discussions/Break
  • 15:00 – 15:40: Markus Myllyoja
  • 15:40 – 16:20: Discussions/Break
  • 16:20 – 17:00: Simon Baker
  • 17:00 – 17:15: Discussions

Titles and Abstracts

  • Simon Baker (Loughborough)
    • Polynomial Fourier decay for fractal measures and their pushforwards
    • Abstract: Determining whether a measure is Rajchman, and if it is, a rate at which the Fourier transform converges to zero, is an important problem. In this talk I will discuss this problem in the setting of stationary measures arising from iterated function systems. I will discuss a recent result which states that if an analytic IFS acting on R does not consist entirely of affine maps, then every self-conformal measure has polynomial Fourier decay. I will then explain how this result can be applied to shrinking target problems. This talk will be based upon joint work with Amlan Banaji and Tuomas Sahlsten.
  • Markus Myllyoja (Oulu)
    • Title: Hausdorff dimension of random covering sets generated by balls
    • Abstract: We consider the Hausdorff dimension of random covering sets generated by balls and driven by general measures. We improve a lower bound given by Ekström and Persson in 2018, extend it to generating balls with an arbitrary sequence of radii and prove their conjecture concerning the exact value of dimension in the special case of radii $n^{-\alpha}$ for a certain parameter range. Further, we show that the natural extension of the conjecture is not true for generating balls with an arbitrary sequence of radii. We also give various examples demonstrating the complexity of dimension in this general case. This is joint work with Esa Järvenpää, Maarit Järvenpää and Örjan Stenflo.
  • Xintian Zhang (Bristol)
    • Hausdorff dimension of the set of eventually always hitting points on a self-conformal set
    • Abstract: Recurrence problems are fundamental in dynamics, and for example, sizes of the set of points recurring infinitely often to a target have been studied extensively in many contexts. For example, the problem for shrinking target set on iterated function system is an active research area. In the current work, we consider a set with a finer recurrence quality, the eventually always hitting set. In a sense, the points in the intersection of an eventually always hitting set and a shrinking target set not only return infinitely often but also at a bounded rate. We study this set in the context of self-conformal iterated function systems, and compute upper and lower bounds for its Hausdorff dimension. Additionally, as an intermediate theorem, we obtain a Hausdorff dimension result for the intersection of eventually always hitting and shrinking target sets.