# Algebra seminar by Iker de las Heras

On Wednesday the 22nd of January 2020, Iker delas Heras (University of the Basque Country) will be visiting the Charlotte Scott Centre for Algebra and giving a talk at 4.30pm in INB3305. The details of his talk are as follows:

Title: 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 a 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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