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SUMMARY:Groups at Infinity and Z-structures - Henrique Souza\, Universidad
  Autónoma de Madrid
DTSTART:20250516T150000Z
DTEND:20250516T160000Z
UID:TALK229486@talks.cam.ac.uk
CONTACT:Julian Wykowski
DESCRIPTION:The motto of geometric group theory is to understand a group b
 y means of its geometry - that is\, its action on geometric spaces. In geo
 metric spaces that show some form of negative curvature\, there is consist
 ently a notion of "boundary" at infinity\, be it the Gromov boundary for h
 yperbolic spaces or the visual boundary for CAT(0) spaces. It is not uncom
 mon for the dynamics of the group action on this boundary to reflect prope
 rties of the group\, such as its dimension or the existence of certain dec
 ompositions. What about general groups? How does one make sense of the "sp
 ace at infinity"? In this talk\, I want to present the notion of a Z-struc
 ture which aims to generalize the notion of boundary for a finitely presen
 ted group. Introduced by M. Bestvina in the 90's\, this structure encapsul
 ates various properties of the Gromov and visual boundaries while at the s
 ame time allowing for more general classes of groups. The main goal of thi
 s introductory talk is to illustrate the concept with examples and some of
  the main results in the theory.\nLooking forward to seeing everyone there
 !
LOCATION:MR13
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