Istvan Kolossvary (Renyi Insitute)

Title: Assouad spectrum of planar carpets

Abstract: There are plenty of examples of sets, such as planar carpets, whose box and Assouad dimensions are different. The Assouad spectrum is a one parameter family of dimensions which gives additional information about the fine scale geometry of such sets. In the talk, we will present a formula for the Assouad spectrum of Gatzouras-Lalley carpets. We will highlight why it can be expressed as the concave conjugate of an explicit piecewise-analytic function and, among dynamically invariant sets, what novel features does the spectrum exhibit. Based on joint work with A. Banaji, J.M. Fraser and A. Rutar.