Speaker: Jeremy Tyson

Title: Quasiconformal distortion of Assouad-type dimensions

Abstract: The study of quasiconformal distortion of Hausdorff dimension dates back to work of Gehring and Väisälä in the 1970s. For planar mappings, sharp distortion bounds follow from the celebrated higher Sobolev integrability theorem of Astala (1994). Such questions are also of interest for other notions of dimension, e.g., box-counting (Minkowski) dimension, Assouad dimension, and related interpolating quantities such as the Assouad spectrum. Building on prior work of Kaufman and the speaker, we obtain explicit, dilatation-dependent estimates for the quasiconformal distortion of the Assouad dimension and the Assouad spectrum for subsets of Euclidean domains. As an application, we identify the optimal dilatation for the quasiconformal equivalence of planar polynomial spirals. This talk is based in part on joint work with Efstathios Chrontsios.