Group Theory Seminar

Hausdorff dimension and Hausdorff spectra in profinite groups

Speaker:  Iker de las Heras (Universidad del País Vasco)
Date:  Tuesday, 23 May 2023 - 11:30
Place:  Aula Gris 2, ICMAT


The Hausdorff dimension is a generalisation of the usual concept of dimension that 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. We will place special emphasis on the so-called (normal) Hausdorff spectra of a given profinite group, as well as in the lower \(p\)-series of \(p\)-adic analytic groups.

Joint work with Benjamin Klopsch and Anitha Thillaisundaram.