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We study the -algebras and von Neumann algebras associated with the universal discrete quantum groups. They give rise to full prime factors and simple exact -algebras. The main tool in our work is the study of an amenable boundary action, yielding the Akemann-Ostrand property. Finally, this boundary can be identified with the Martin or the Poisson boundary of a quantum random walk
Let be the space of projective structures on a closed surface of genus , and let be the subset of of projective structures with quasi-Fuchsian holonomy. It is known that consists of infinitely many connected components. In this article, we show that the closure of any exotic component of is not a topological manifold with boundary and that any two components of have intersecting closures
In this article, we make the first steps toward developing a theory of intersections of coisotropic submanifolds, similar to that for Lagrangian submanifolds.
For coisotropic submanifolds satisfying a certain stability requirement, we establish persistence of coisotropic intersections under Hamiltonian diffeomorphisms, akin to the Lagrangian intersection property. To be more specific, we prove that the displacement energy of a stable coisotropic submanifold is positive, provided that the ambient symplectic manifold meets some natural conditions. We also show that a displaceable, stable, coisotropic submanifold has nonzero Liouville class. This result further underlines the analogy between displacement properties of Lagrangian and coisotropic submanifolds
We establish global well-posedness and scattering for solutions to the defocusing mass-critical (pseudoconformal) nonlinear Schrödinger equation for large, spherically symmetric, initial data in dimensions . After using the concentration-compactness reductions in  to reduce to eliminating blow-up solutions that are almost periodic modulo scaling, we obtain a frequency-localized Morawetz estimate and exclude a mass evacuation scenario (somewhat analogously to , , ) in order to conclude the argument
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