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SUMMARY:Profinite completions of groups acting on rooted trees - Alejandra
  Garrido (Universidad Complutense de Madrid)
DTSTART:20250731T143000Z
DTEND:20250731T153000Z
UID:TALK234301@talks.cam.ac.uk
DESCRIPTION:Groups that act faithfully on rooted trees can be completed in
  different ways to obtain profinite groups. The profinite completion of th
 e group maps onto each of them. Determining the kernels of these maps is k
 nown as the congruence subgroup problem\, by analogy with a similar proble
 m in arithmetic groups. This problem has been studied by various authors o
 ver the years\, most notably for self-similar groups and (weakly) branch g
 roups. In the case of self-similar regular branch groups\, much insight ca
 n be gained into this problem using a symbolic-dynamical point of view.\nA
 fter reviewing some of the known results on the congruence subgroup proble
 m for various combinations of self-similar and (weakly) branch groups\, I 
 plan to talk on joint work with Zoran Sunic where we use the symbolic-dyna
 mical approach to describe explicitly one of the kernels of the congruence
  subgroup problem\, for certain self-similar branch groups.\nExamples will
  be given. No previous knowledge of self-similar or branch groups is requi
 red.
LOCATION:Seminar Room 1\, Newton Institute
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