Assouad-type dimensions: finer information on scaling and homogeneity

Abstract: The Assouad dimension is a notion of dimension which captures the worst-case scaling of a set at all locations and all scales. However, in many situations the Assouad dimension measures scaling in a way which is too coarse, and quantifying the precise resolution at which larger-than-average scaling occurs has been important in applications. In this talk, I will give an introduction and overview of recent work on variations of the Assouad dimension. I will also touch on some recent applications in the literature including: large deviations of branching processes, smoothness of iterated function system attractors, quasi-conformal distortion of sets, and $L^p$-improving properties of maximal operators with restricted dilation sets.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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