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SUMMARY:Strong ergodicity versus spectral gap for group actions on measure
  spaces
DTSTART:20180524T130000
DTEND:20180524T140000
DTSTAMP:20260509T131735Z
UID:1c38ef037663d8f360f29a1a7e398ee070edd70569a651ddc87f07a9
CATEGORIES:Conferences - Seminars
DESCRIPTION:Cyril Houdayer (Université de Paris-Sud)\nIt is well-known th
 at for probability measure preserving (pmp) group actions\, if the associa
 ted Koopman representation has spectral gap (i.e. has no almost invariant 
 vectors)\, then the action is strongly ergodic (i.e. has no non-trivial al
 most invariant measurable subsets). The converse is however not true as de
 monstrated by Schmidt’s example.\n\n \n\nIn this talk\, I will present 
 a characterization of strong ergodicity for arbitrary nonsingular group ac
 tions in terms of a spectral gap property of the full group of the associa
 ted orbit equivalence relation. I will then explain how this criterion can
  be used to characterize strong ergodicity of the Maharam extension of gro
 up actions of type III in terms of a new invariant\, analogous to Connes t
 au invariant for von Neumann type III factors. This is joint work with A. 
 Marrakchi and P. Verraedt.
LOCATION:MA A3 30 https://plan.epfl.ch/?room=MAA330
STATUS:CONFIRMED
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