Browsing by Author "de Laat, Tim"

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    Mini-Workshop: Superexpanders and Their Coarse Geometry
    (Zürich : EMS Publ. House, 2018) de Laat, Tim; de la Salle, Mikael
    It is a deep open problem whether all expanders are superexpanders. In fact, it was already a major challenge to prove the mere existence of superexpanders. However, by now, some classes of examples are known: Lafforgue’s expanders constructed as sequences of finite quotients of groups with strong Banach property (T), the examples coming from zigzag products due to Mendel and Naor, and the recent examples coming from group actions on compact manifolds. The methods which are used to construct superexpanders are typically functional analytic in nature, but also rely on arguments from geometry and combinatorics. Another important aspect of the study of superexpanders is their (coarse) geometry, in particular in order to distinguish them from each other. The aim of this workshop was to bring together researchers working on superexpanders and their coarse geometry from different perspectives, with the aim of sharing expertise and stimulating new research.
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    Weak*-Continuity of Invariant Means on Spaces of Matrix Coefficients
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2021) de Laat, Tim; Zadeh, Safoura
    With every locally compact group G, one can associate several interesting bi-invariant subspaces X(G) of the weakly almost periodic functions WAP(G) on G, each of which captures parts of the representation theory of G. Under certain natural assumptions, such a space X(G) carries a unique invariant mean and has a natural predual, and we view the weak∗-continuity of this mean as a rigidity property of G. Important examples of such spaces X(G), which we study explicitly, are the algebra McbAp(G) of p-completely bounded multipliers of the Figà-Talamanca-Herz algebra Ap(G) and the p-Fourier-Stieltjes algebra Bp(G). In the setting of connected Lie groups G, we relate the weak∗-continuity of the mean on these spaces to structural properties of G. Our results generalise results of Bekka, Kaniuth, Lau and Schlichting.