SMRI Seminar: Wormell -- Hausdorff dimension of the Apollonian gasket

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.