Alex Rutar

Assouad-type dimensions


Assouad-type dimensions are a family of dimensions which capture the “coarsest” scaling properties of a set. This area has been very active recently, with a large amount of interest in this field from various points of view, such as conformal geometry, embedding theory, and fractal geometry.

In this area, I have proven classification results for Assouad spectra and studied the Assouad dimension of overlapping self-affine carpets in my joint paper with Jonathan Fraser.

Relevant Publications

  1. Assouad-type dimensions of overlapping self-affine sets
    With: Jonathan M. Fraser
    Journal: Preprint (submitted)
    Links: pdfarxiv
  2. Attainable forms of Assouad spectra
    Journal: Indiana Univ. Math. J. (to appear)
    Links: pdfarxiv