58 citations · 599 across the 43 of their papers we have counts for
45 papers
The noncommutative topological factor theorem for rank-one product lattices
Cyril Houdayer, Corentin Le Bars
We prove a noncommutative topological factor theorem for irreducible lattices in products of real rank-one simple Lie groups. The intermediate C*-subalgebras between the reduced gr…
Selfless W-probability spaces and Connes' bicentralizer problem
Cyril Houdayer, Amine Marrakchi
We introduce the notion of selfless W-probability space and study its connection with Connes' bicentralizer problem. In particular, we show that if is a separable type ${\r…
Operator algebraic characterization of the noncommutative Poisson boundary
Cyril Houdayer
We obtain an operator algebraic characterization of the noncommutative Furstenberg-Poisson boundary associated w…
The noncommutative factor theorem for lattices in product groups
Rémi Boutonnet, Cyril Houdayer
We prove a noncommutative Bader-Shalom factor theorem for lattices with dense projections in product groups. As an application of this result and our previous works, we obtain a no…
Pointwise inner automorphisms of almost periodic factors
Cyril Houdayer, Yusuke Isono
We prove that a large class of nonamenable almost periodic type factors , including all McDuff factors that tensorially absorb and all free Araki-Woods…
Charmenability of higher rank arithmetic groups
Uri Bader, Rémi Boutonnet, Cyril Houdayer
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 group…
Noncommutative ergodic theory of higher rank lattices
Cyril Houdayer
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…
Existentially closed W*-probability spaces
Isaac Goldbring, Cyril Houdayer
We study several model-theoretic aspects of W-probability spaces, that is, -finite von Neumann algebras equipped with a faithful normal state. We first study the existential…
Charmenability of arithmetic groups of product type
Uri Bader, Rémi Boutonnet, Cyril Houdayer +1
We discuss special properties of the spaces of characters and positive definite functions, as well as their associated dynamics, for arithmetic groups of product type. Axiomatizing…
Examples of property (T) II factors with trivial fundamental group
Ionut Chifan, Sayan Das, Cyril Houdayer +1
In this article we provide the first examples of property (T) factors with trivial fundamental group, . Our examples arise as gro…
Connes' bicentralizer problem for q-deformed Araki-Woods algebras
Cyril Houdayer, Yusuke Isono
Let be any strongly continuous orthogonal representation of on a real (separable) Hilbert space . For any , we den…
Stationary characters on lattices of semisimple Lie groups
Rémi Boutonnet, Cyril Houdayer
We show that stationary characters on irreducible lattices of higher-rank connected semisimple Lie groups are conjugation invariant, that is, they are genuine characters. Th…
Structure of extensions of free Araki-Woods factors
Cyril Houdayer, Benjamin Trom
We investigate the structure of crossed product von Neumann algebras arising from Bogoljubov actions of countable groups on Shlyakhtenko's free Araki-Woods factors. Among other res…
Structure of bicentralizer algebras and inclusions of type III factors
Hiroshi Ando, Uffe Haagerup, Cyril Houdayer +1
We investigate the structure of the relative bicentralizer algebra for inclusions of von Neumann algebras with normal expectation where is a type ${\r…
Factoriality, Connes' type III invariants and fullness of amalgamated free product von Neumann algebras
Cyril Houdayer, Yusuke Isono
We investigate factoriality, Connes' type invariants and fullness of arbitrary amalgamated free product von Neumann algebras using Popa's deformation/rigidity theory. A…
Strongly ergodic equivalence relations: spectral gap and type III invariants
Cyril Houdayer, Amine Marrakchi, Peter Verraedt
We obtain a spectral gap characterization of strongly ergodic equivalence relations on standard measure spaces. We use our spectral gap criterion to prove that a large class of ske…
Singular MASAs in type III factors and Connes' Bicentralizer Property
Cyril Houdayer, Sorin Popa
We show that any type factor with separable predual satisfying Connes' Bicentralizer Property (CBP) has a singular maximal abelian -subalgebra that is the range…
Locally compact groups acting on trees, the type I conjecture and non-amenable von Neumann algebras
Cyril Houdayer, Sven Raum
We address the problem to characterise closed type I subgroups of the automorphism group of a tree. Even in the well-studied case of Burger-Mozes' universal groups, non-type I crit…
Fullness and Connes' invariant of type III tensor product factors
Cyril Houdayer, Amine Marrakchi, Peter Verraedt
We show that the tensor product of any two full factors and (possibly of type ) is full and we compute Connes' invariant $τ(M…
Amenable absorption in amalgamated free product von Neumann algebras
Rémi Boutonnet, Cyril Houdayer
We investigate the position of amenable subalgebras in arbitrary amalgamated free product von Neumann algebras . Our main result states that under natural analy…
Optimal quantizers for a nonuniform distribution on a Sierpinski carpet
Mrinal Kanti Roychowdhury
The purpose of quantization for a probability distribution is to estimate the probability by a discrete probability with finite support. In this paper, a nonuniform probability mea…
Structure of modular invariant subalgebras in free Araki-Woods factors
Rémi Boutonnet, Cyril Houdayer
We show that any amenable von Neumann subalgebra of any free Araki-Woods factor that is globally invariant under the modular automorphism group of the free quasi-free state is nece…
Strong solidity of free Araki-Woods factors
Rémi Boutonnet, Cyril Houdayer, Stefaan Vaes
We show that Shlyakhtenko's free Araki-Woods factors are strongly solid, meaning that for any diffuse amenable von Neumann subalgebra that is the range of a normal conditional expe…
Bi-exact groups, strongly ergodic actions and group measure space type III factors with no central sequence
Cyril Houdayer, Yusuke Isono
We investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras arising from arbitrary actions of bi-exa…