# Algebra seminar in Lincoln: talk by Iker de las Heras

On the 22nd of January 2020, **Iker de las Heras (University of the Basque Country)** visited Charlotte Scott Centre for Algebra and gave a talk “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. In this talk we will introduce this concept of the Hausdorff dimension in such groups and we will overview some of its 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.

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