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SUMMARY:Alejandra Garrido (Universidad Autónoma de Madrid)
DTSTART:20211202T170000Z
DTEND:20211202T180000Z
DTSTAMP:20260423T021323Z
UID:GOThIC/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOThIC/45/">
 On various profinite completions of groups acting on rooted trees</a>\nby 
 Alejandra Garrido (Universidad Autónoma de Madrid) as part of GOThIC - Is
 chia Online Group Theory Conference\n\n\nAbstract\nGroups that act faithfu
 lly on rooted trees can be studied via their finite quotients. There are s
 everal natural collections of finite quotients that can be chosen for this
 . The mathematical object that encodes all these finite quotients and the 
 maps between them is the profinite completion of the group (with respect t
 o the chosen collection). Taking all possible finite quotients of the grou
 p gives *the* profinite completion of the group\, annd this maps onto each
  of the other completions. Determining the kernels of these maps is known 
 as the congruence subgroup problem.  This has been studied by various aut
 hors over the last few years\, most notably for self-similar groups and (w
 eakly) branch groups. In the case of self-similar regular branch groups\, 
 much insight can be gained into this problem using a symbolic-dynamical po
 int of view. After reviewing the problem and previous work on it\, I will 
 report on work in progress with Zoran Sunic on determining the dynamical c
 omplexity of these completions and calculating some of these kernels with 
 relative ease.\n\nExamples will be given. No previous knowledge of profini
 te\, self-similar or branch groups is required.\n
LOCATION:https://researchseminars.org/talk/GOThIC/45/
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