Alex Rutar

Dimension classification


Dimension classification is concerned with determining the possible forms and configurations of various dimensional quantities, either for general sets or within specific families.

In my joint project with Amlan Banaji we develop general techniques for constructing homogeneous Moran sets, and apply these techniques to classify the possible forms of intermediate dimensions. Then, using the same techniques along with some new constructions, I obtain classification results for the Assouad spectra and construct some sets with exceptional properties.

Relevant Publications

  1. Attainable forms of Assouad spectra
    Journal: Indiana Univ. Math. J. (to appear)
    Links: pdfarxiv
  2. Attainable forms of intermediate dimensions
    With: Amlan Banaji
    Journal: Ann. Fenn. Math. 47 (2022), 939–960
    Links: pdfdoiarxiv