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SUMMARY:Ergodic states on type III_1 factors and ergodic actions - Stefaan
  Vaes (KU Leuven)
DTSTART:20230626T090000Z
DTEND:20230626T100000Z
UID:TALK201964@talks.cam.ac.uk
DESCRIPTION:I will report on a joint work with Amine Marrakchi. Since the 
 early days of Tomita-Takesaki theory\, it is known that a von Neumann alge
 bra that admits a state with trivial centralizer must be a type III_1 fact
 or\, but the converse remained open. I will present a solution of this pro
 blem\, proving that such ergodic states form a dense G_\\delta set among a
 ll faithful normal states on any III_1 factor with separable predual. Thro
 ugh Connes' Radon-Nikodym cocycle theorem\, this problem is related to the
  existence of ergodic cocycle perturbations for outer group actions\, whic
 h I will discuss in the second half of the talk.
LOCATION:Seminar Room 1\, Newton Institute
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