Tim de Laat
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View article: Spectral gap and origami expanders
Spectral gap and origami expanders Open
We construct the first measure-preserving affine actions with spectral gap on surfaces of arbitrary genus g > 1 . We achieve this by finding geometric representatives of multi-twists on origami surfaces. As a major application, we construc…
View article: Dynamical propagation and Roe algebras of warped spaces
Dynamical propagation and Roe algebras of warped spaces Open
Given a non-singular action $Γ\curvearrowright (X,μ)$, we define the $*$-algebra $\mathbb C_{\rm fp}[Γ\curvearrowright X]$ of operators of finite dynamical propagation associated with this action. This assignment is completely canonical an…
View article: Unitary $L^{p+}$-representations of almost automorphism groups
Unitary $L^{p+}$-representations of almost automorphism groups Open
Let $G$ be a locally compact group with an open subgroup $H$ with the Kunze-Stein property, and let $π$ be a unitary representation of $H$. We show that the representation $\widetildeπ$ of $G$ induced from $π$ is an $L^{p+}$-representation…
View article: Actions of higher rank groups on uniformly convex Banach spaces
Actions of higher rank groups on uniformly convex Banach spaces Open
We prove that all isometric actions of higher rank simple Lie groups and their lattices on arbitrary uniformly convex Banach spaces have a fixed point. This vastly generalises a recent breakthrough of Oppenheim. Combined with earlier work …
View article: Spectral gap and origami expanders
Spectral gap and origami expanders Open
We construct the first measure-preserving affine actions with spectral gap on surfaces of arbitrary genus $g > 1$. We achieve this by finding geometric representatives of multi-twists on origami surfaces. As a major application, we constru…
View article: Group $C^*$-algebras of locally compact groups acting on trees
Group $C^*$-algebras of locally compact groups acting on trees Open
We study the group $C^*$-algebras $C^*_{L^{p+}}(G)$ - constructed from $L^p$-integrability properties of matrix coefficients of unitary representations - of locally compact groups $G$ acting on (semi-)homogeneous trees of sufficiently larg…
View article: The Fourier algebra of a rigid $C^{\ast}$-tensor category
The Fourier algebra of a rigid $C^{\ast}$-tensor category Open
Completely positive and completely bounded mutlipliers on rigid $C^{\ast}$-tensor categories were introduced by Popa and Vaes. Using these notions, we define and study the Fourier-Stieltjes algebra, the Fourier algebra and the algebra of c…
View article: On strong property (T) and fixed point properties for Lie groups
On strong property (T) and fixed point properties for Lie groups Open
We consider certain strengthenings of property (T) relative to Banach spaces. Let be a Banach space for which the Banach–Mazur distance to a Hilbert space of all -dimensional subspaces grows as a power of strictly less than one half. We …
View article: Strong property (T) for higher-rank simple Lie groups: Figure 1.
Strong property (T) for higher-rank simple Lie groups: Figure 1. Open
We prove that connected higher rank simple Lie groups have Lafforgue's strong\nproperty (T) with respect to a certain class of Banach spaces\n$\\mathcal{E}_{10}$ containing many classical superreflexive spaces and some\nnon-reflexive space…
View article: Approximation properties for noncommutative <i>L<sup>p</sup> </i>-spaces of high rank lattices and nonembeddability of expanders
Approximation properties for noncommutative <i>L<sup>p</sup> </i>-spaces of high rank lattices and nonembeddability of expanders Open
This article contains two rigidity type results for SL ( n , ℤ ) {\mathrm{SL}(n,\mathbb{Z})} for large n that share the same proof. Firstly, we prove that for every p ∈ [ 1 , ∞ ] {p\in[1,\infty]} different from 2, the noncomm…