Title: Abelian-like properties in *p*-groups

Abstract: An important idea in the theory of *p*-groups has been finding families with desirable properties, such as those enjoyed by abelian groups. In this light we consider groups which are ‘powerful’ in the sense of Lubotzky and Mann. We introduce some variants of powerful *p*-groups and explore some of their most interesting properties.

With the aim of making this talk as accessible as possible, we will begin by recalling some basic properties of *p*-groups and motivation for studying them.

*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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Title: Leighton’s graph covering theorem

Abstract: Leighton’s theorem for graphs states that any pair of finite graphs with common universal covers have a common finite cover.

Equivalently, this says that any pair of uniform lattices in the automorphism groups of a tree can be commensurated.

I will discuss the significance of this theorem, recent generalizations, and how it can be applied in geometric group theory.

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On 15th of January, Professor Marcus du Sautoy OBE FRS (University of Oxford) delivered the 5th Annual Boole Lecture “The Creativity Code“. At…]]>

On 15th of January, **Professor Marcus du Sautoy OBE FRS (University of Oxford)** delivered the 5th Annual Boole Lecture “The Creativity Code“. At the beginning Prof Evgeny Khukhro introduced the lecturer, a prominent algebraist, who is also very well known for his work popularising science and mathematics on radio, TV, and in print. This lecture raised very interesting questions on the role that Artificial Intelligence already plays in the human society and on the prospects of AI acquiring even greater powers and roles in most creative areas of human life. The 500 seat auditorium was filled to the capacity with diverse audience consisting of staff, students and members of the public. At several points of the lecture, Marcus interacted with the audience, using online polling via mobile devices. Afterwards numerous questions and comments spilled over to the atrium of Isaac Newton Building, where a bookstall…

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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. ]]>

**Ischia Group Theory 2020**”, which will take place in Ischia (Italy), from 30th of March to 4th of April, 2020. This biannual conference is one of the major events in the academic calendar attracting experts in group theory from all over the world.

Anitha was also visiting Benjamin Klopsch and Moritz Petschick at Duesseldorf to further some collaborations.

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