Title
Lower Assouad-type dimensions and spectra: Theory and recent progress
Abstract
Fractal dimensions and dimension spectra are fundamental to fractal geometry. Recently, the study of dimension spectra has emerged as an active topic, yielding a wide range of significant results. This talk begins with a review of standard dimension definitions. We then focus on the lower Assouad dimension (also known as the uniformity dimension) and its variations, collectively known as lower Assouad-type dimensions. We discuss these concepts, including the lower Assouad spectrum, in the context of characterizing the local separation of fractal sets. In particular, we present recent results regarding attainable forms and dimension interpolations.
