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SUMMARY:Sven Raum (Stockholm University)
DTSTART:20210809T063000Z
DTEND:20210809T073000Z
DTSTAMP:20260423T021442Z
UID:SiN/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SiN/27/">Loc
 ally compact groups acting on trees\, the type I conjecture and non-amenab
 le von Neumann algebras</a>\nby Sven Raum (Stockholm University) as part o
 f Symmetry in Newcastle\n\n\nAbstract\nn the 90's\, Nebbia conjectured tha
 t a group of tree automorphisms acting transitively on the tree's boundary
  must be of type I\, that is\, its unitary representations can in principa
 l be classified.  For key examples\, such as Burger-Mozes groups\, this co
 njecture is verified.  Aiming for a better understanding of Nebbia's conje
 cture and a better understanding of representation theory of groups acting
  on trees\, it is natural to ask whether there is a characterisation of ty
 pe I groups acting on trees. In 2016\, we introduced in collaboration with
  Cyril Houdayer a refinement of Nebbia's conjecture to a trichotomy\, oppo
 sing type I groups with groups whose von Neumann algebra is non-amenable. 
  For large classes of groups\, including Burger-Mozes groups\, we could ve
 rify this trichotomy.\nIn this talk\, I will motivate and introduce the co
 njecture trichotomy for groups acting on tress and explain how von Neumann
  algebraic techniques enter the picture.\n
LOCATION:https://researchseminars.org/talk/SiN/27/
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