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SUMMARY:Real cubings - Ilya Kazachkov (Bilbao)
DTSTART:20241108T134500Z
DTEND:20241108T144500Z
UID:TALK220993@talks.cam.ac.uk
CONTACT:Macarena Arenas
DESCRIPTION:The theory of real trees and groups acting on them has had a d
 eep impact on group theory: by providing tools to attack new problems\, si
 mplifying proofs\, and establishing new connections between group theory a
 nd geometry\, topology\, dynamical systems\, and model theory.  \n\nIn thi
 s talk\, we will introduce a new class of metric spaces\, called real cubi
 ngs\, which we regard as higher-dimensional real trees\, and characterise 
 them inside the class of median spaces. As hyperbolic groups are linked to
  real trees via their asymptotic cones\, we will show that real cubings ar
 e related to hierarchically hyperbolic groups\, a class of groups that con
 tains right-angled Artin groups and the mapping class groups of closed sur
 faces.\n\nWe will then describe the structure of universal real cubings an
 d prove that there exists a group that has a free and transitive action on
  a given universal real cubing.\n\nThis is joint work with Montse Casals-R
 uiz and Mark Hagen.
LOCATION:MR13
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