• Corpus ID: 239009785

Noncommutative ergodic theory of higher rank lattices

@inproceedings{Houdayer2021NoncommutativeET,
  title={Noncommutative ergodic theory of higher rank lattices},
  author={Cyril Houdayer},
  year={2021}
}
We survey recent results regarding the study of dynamical properties of the space of positive definite functions and characters of higher rank lattices. These results have several applications to ergodic theory, topological dynamics, unitary representation theory and operator algebras. The key novelty in our work is a dynamical dichotomy theorem for equivariant faithful normal unital completely positive maps between noncommutative von Neumann algebras and the space of bounded measurable… 

References

SHOWING 1-10 OF 58 REFERENCES
Charmenability of higher rank arithmetic groups
We complete the study of characters on higher rank semisimple lattices initiated in [BH19, BBHP20], the missing case being the case of lattices in higher rank simple algebraic groups in arbitrary
RIGIDITY FOR VON NEUMANN ALGEBRAS
  • A. Ioana
  • Mathematics
    Proceedings of the International Congress of Mathematicians (ICM 2018)
  • 2019
We survey some of the progress made recently in the classification of von Neumann algebras arising from countable groups and their measure preserving actions on probability spaces. We emphasize
Deformation and rigidity for group actions and von Neumann algebras
We present some recent rigidity results for von Neumann algebras (II1 factors) and equivalence relations arising from measure preserving actions of groups on probability spaces which satisfy a
Rigidity for von Neumann algebras and their invariants
We give a survey of recent classification results for crossed product von Neumann algebras arising from measure preserving group actions on probability spaces. This includes II_1 factors with
Character rigidity for lattices in higher-rank groups
We show that if Γ is an irreducible lattice in a higher rank center-free semi-simple Lie group with no compact factors and having property (T) of Kazhdan, then Γ is operator algebraic superrigid,
Lyapunov indices of a product of random matrices
CONTENTS Introduction § 1. The multiplicative ergodic theorem § 2. Quasi-projective transformations § 3. Contraction property of a semigroup § 4. Invariant measure and lemmas on convergence § 5.
Stabilizers for ergodic actions of higher rank semisimple groups
Let G be a connected semisimple Lie group with finite center and R-rank > 2. Suppose that each simple factor of G either has R-rank > 2 or is locally isomorphic to Sp(l, n) or F4(-20). We prove that
Classification and rigidity for von Neumann algebras
In this talk, I will survey recent progress made on the classification of von Neumann algebras arising from countable groups and their actions on probability spaces. In particular, I will present the
A Normal Subgroup Theorem for Commensurators of Lattices
We establish a general normal subgroup theorem for commensurators of lattices in locally compact groups. While the statement is completely elementary, its proof, which rests on the original strategy
A structure theorem for actions of semisimple Lie groups
We consider a connected semisimple Lie group G with finite center, an admissible probability measure , on G, and an ergodic (G, ,u)-space (X, v). We first note (Lemma 0.1) that (X, v) has a unique
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