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SUMMARY:Shuoxing Zhou (École Normale Supérieure)
DTSTART:20241113T200000Z
DTEND:20241113T210000Z
DTSTAMP:20260420T053532Z
UID:NYC-NCG/181
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/181/
 ">Noncommutative topological boundaries and amenable invariant intermediat
 e subalgebras</a>\nby Shuoxing Zhou (École Normale Supérieure) as part o
 f Noncommutative geometry in NYC\n\n\nAbstract\nAs an analogue of the topo
 logical boundary of discrete groups $\\Gamma$\, we define the noncommutati
 ve topological boundary of tracial von Neumann algebras $(M\,\\tau)$ and a
 pply it to generalize a recent result by Amrutam-Hartman-Oppelmayer\, show
 ing that for a trace preserving action $\\Gamma \\curvearrowright (A\,\\ta
 u_A)$ on an amenable tracial von Neumann algebra\, any $\\Gamma$-invariant
  amenable intermediate subalgebra between $A$ and $\\Gamma\\ltimes A$ is n
 ecessarily a subalgebra of $\\mathrm{Rad}(\\Gamma) \\ltimes A$. By taking 
 $(A\,\\tau_A)=L^\\infty(X\,\\nu_X)$ for a free pmp action $\\Gamma \\curve
 arrowright (X\,\\nu_X)$\, we obtain a similar result for invariant subequi
 valence relations of $\\mathcal{R}_{\\Gamma \\curvearrowright X}$.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/181/
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