Hausdorff spectrum of p-adic analytic pro-p groups

Anitha Thillaisundaram (Lund University)

Monday 8th April 15:00-16:00 Maths 311B

Abstract

The concept of Hausdorff dimension first arose in the context of fractals. With time it was also applied to other areas of mathematics, and this was extended in the 90s to profinite groups. A special class of profinite groups includes the p-adic analytic groups, which have a rich geometric and analytic structure, and play a key role in the theory of groups. It is an open question still whether p-adic analytic groups can be characterised by the set of Hausdorff dimensions of their subgroups, i.e. the so-called Hausdorff spectrum. In this talk, we survey what has been done towards answering this question, and we include recent results concerning the Hausdorff spectrum when computed with respect to the lower p-series. This is joint work with Iker de las Heras and Benjamin Klopsch.

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