The Hausdorff dimensions of branch groups

The concept of Hausdorff dimension was defined in the 1930s and
was originally applied to fractals and shapes in nature. However, from the
work of Abercrombie, Barnea and Shalev in the 1990s, the computation of
the Hausdorff dimensions in profinite groups has been made possible.
Starting with Abert and Virag's well-known result that there are groups
acting on a rooted tree with all possible Hausdorff dimensions,
mathematicians have been interested in computing the Hausdorff dimensions
of explicit families of groups acting on rooted trees, and in particular,
of the so-called branch groups. Branch groups first appeared in the
context of the Burnside problem, where they delivered the first explicit
examples of finitely generated infinite torsion groups. Since then, branch
groups have gone on to play a key role in group theory and beyond. In this
talk, we will survey known results concerning the Hausdorff dimensions of
branch groups, in particular mentioning some recent joint work Gustavo
Fernandez-Alcober and Sukran Gul.
 

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https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062