This seminar series gives visitors and staff members the opportunity to explain the context and aims of their work. These research talks cover any field in the mathematical sciences, and should be presented in a way that is understandable and interesting to a broad audience. Seminar information and recordings can be found below and in the SMRI Seminar YouTube playlist.
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SMRI Seminar ‘Hausdorff dimension of the Apollonian gasket’
Caroline Wormell, The University of Sydney
Thursday 27 February 2025
Abstract: The Apollonian gasket is a well-studied circle packing, created by iteratively filling a region with mutually tangent circles. Important properties of the packing, including the distribution of the circle radii, are universal and governed by its Hausdorff dimension. No closed form is currently known for the Hausdorff dimension, and its computation is a special case of a more general and hard problem: effective, rigorous estimates of dimension of a limit set generated by non-uniform contractions. In this talk, I will talk about an efficient method for solving this problem. With this method we can not only compute the dimension of the gasket to a lot of decimal places, but also rigorously validate this computation as a mathematical theorem. Our method is not particularly specialised to the Apollonian gasket, and could generalise easily to other “difficult” parabolic fractals. Based on joint work with Polina Vytnova.