First ℓ2-Betti numbers and proper proximality
C Ding - Advances in Mathematics, 2024 - Elsevier
We show that for a countable exact group, having positive first ℓ 2-Betti number implies
proper proximality in this sense of [3]. This is achieved by showing a cocycle superrigidity …
proper proximality in this sense of [3]. This is achieved by showing a cocycle superrigidity …
Rigid Graph Products
M Borst, M Caspers, E Chen - arXiv preprint arXiv:2408.06171, 2024 - arxiv.org
We prove rigidity properties for von Neumann algebraic graph products. We introduce the
notion of rigid graphs and define a class of II $ _1 $-factors named $\mathcal {C} _ {\rm …
notion of rigid graphs and define a class of II $ _1 $-factors named $\mathcal {C} _ {\rm …
General solidity phenomena and anticoarse spaces for type factors
By developing a theory of anticoarse spaces in the purely infinite setting and using 1-
bounded entropy techniques along with recent strong convergence results in random matrix …
bounded entropy techniques along with recent strong convergence results in random matrix …
A unique Cartan subalgebra result for Bernoulli actions of weakly amenable groups
C Ding - arXiv preprint arXiv:2404.08182, 2024 - arxiv.org
We show that if $\Gamma\curvearrowright (X^\Gamma,\mu^\Gamma) $ is a Bernoulli action
of an icc nonamenable group $\Gamma $ which is weakly amenable with Cowling …
of an icc nonamenable group $\Gamma $ which is weakly amenable with Cowling …
[PDF][PDF] On rigidity theory, strong solidity, Coxeter groups, graph products and commutator estimates
MJ Borst - 2025 - pure.tudelft.nl
The main topics of this thesis include: von Neumann algebras, Coxeter groups, graph
products, approximation properties, rigidity theory and commutator estimates. We discuss …
products, approximation properties, rigidity theory and commutator estimates. We discuss …