Hausdorff dimension and Hausdorff spectra in profinite groups

Abstract: The Hausdorff dimension is a generalisation of the usual concept of dimension which allows to define the dimension of fractal sets in metric spaces. In the last decades, this notion has led to fruitful applications in the context of countably based profinite groups, as these groups can be naturally seen as metric spaces with respect to a given filtration series.

In this talk we will give a brief introduction to this topic and we will overview some of the main related properties. Finally, we will present some results concerning the so-called (normal) Hausdorff spectra of a given profinite group, which reflect the range of Hausdorff dimensions of closed (normal) subgroups.

Joint work with Benjamin Klopsch and Anitha Thillaisundaram.

group theory

Audience: researchers in the topic

GOThIC - Ischia Online Group Theory Conference

Series comments: Please send a message to andrea.caranti@unitn.it to receive a link to the Zoom room where the conference (a series of talks, actually) takes place.