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SUMMARY:On the profinite topology in branch and weakly branch groups
DTSTART:20261012T120000Z
DTEND:20261012T130000Z
DTSTAMP:20261030T200200Z
UID:indico-event-5941@agenda.irmp.ucl.ac.be
DESCRIPTION:Speakers: Jorge Fariña Asategui (University of Geneva)\n\n \
 n\n\n\nGiven a finitely generated discrete group\, one can define a natura
 l topology on it by declaring finite-index subgroups to form an open neigh
 bourhood of the identity\; this is called the profinite topology. Then\, o
 ne is interested in which subgroups of the group are closed in the profini
 te topology. This leads to the notions of residually finite\, LERF or ERF\
 , depending on whether the trivial subgroup\, all finitely generated subgr
 oups or all subgroups are closed in the profinite topology respectively. R
 esidually finite groups are precisely those acting on rooted spherically h
 omogeneous rooted trees\, while the LERF and ERF properties are much more 
 mysterious in general. A classical result of Hall shows that free groups a
 re LERF\, which was later extended to limit groups by Wilton. Examples of 
 ERF groups are difficult to find\, and they have only been found among vir
 tually polycyclic groups.We will be interested in two well-known classes o
 f groups acting on rooted trees: branch and weakly branch groups. These cl
 asses of groups have played a prominent role in geometric group theory by 
 exhibiting examples of groups of intermediate growth\, amenable but not el
 ementary amenable groups\, and strong links to complex and arithmetic dyna
 mics. The LERF property has been studied for branch groups since the early
  2000s\, but currently only very ad hoc methods are available for the stud
 y of this property. Thus\, the amount of examples of LERF branch groups is
  extremely limited. In this talk\, we shall focus on the ERF property inst
 ead and see what can be said about it for branch and weakly branch groups.
  This is joint work with Paul-Henry Leemann and Tatiana Nagnibeda.\n\n\n\n
  \n\nhttps://agenda.irmp.ucl.ac.be/event/5941/
LOCATION:B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cy
 clotron\, 2\, Louvain-la-Neuve))
URL:https://agenda.irmp.ucl.ac.be/event/5941/
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