Groups and Operator Algebras Seminar

Speaker: Anitha Thillaisundaram (Lund University)

Title: Beauville structures for quotients of infinite Grigorchuk-Gupta-Sidki groups acting on the p^n-adic tree

Abstract: Groups of surfaces isogenous to a higher product of curves can be characterised by a purely group-theoretic condition, which is the existence of a so-called Beauville structure. Gul and Uria-Albizuri showed that quotients of the periodic Grigorchuk-Gupta-Sidki groups, GGS-groups for short, that act on the p-adic tree, admit Beauville structures. Such groups acting on p-adic trees (i.e. rooted trees) first appeared in the context of the Burnside problem, where they delivered the first explicit examples of finitely generated infinite torsion groups. Since then, groups acting on rooted trees have gone on to play a key role in group theory and beyond. In particular, Steinberg and Szakacs have recently given necessary and sufficient conditions for the Nekrashevych algebra of certain GGS-type groups to be simple.

We extend the result of Gul and Uria-Albizuri by showing that quotients of infinite periodic GGS-groups, that act on the p^n-adic tree, also admit Beauville structures for all primes p and positive integers n. This is joint work with Elena Di Domenico and Şükran Gül.

GOA website: https://sites.google.com/view/copenhagen-goa-seminar