Analysis on simple Lie groups and lattices

DOI10.4171/icm2022/160arXiv2204.12381OpenAlexW4309973984MaRDI QIDQ6119190

Mikael de la Salle

Publication date: 22 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.12381

zbMATH Keywords

expander graphsgroup von Neumann algebrasBanach space representationsFourier synthesishigher-rank latticesrank zero reduction

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Harmonic analysis on specific compact groups (43A75) Spaces of operators; tensor products; approximation properties (46B28) Operator spaces and completely bounded maps (46L07) Semisimple Lie groups and their representations (22E46) Convergence of Fourier series and of inverse transforms (43A50)

Cites Work

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• Towards strong Banach property (T) for \(\mathrm{SL}(3,\mathbb R)\)
• Approximation properties for noncommutative \(L^p\)-spaces associated with lattices in Lie groups
• Examples of groups which are not weakly amenable
• Property \(F\ell_q\) implies property \(F\ell_{p}\) for \(1<p<q<\infty\)
• On strong property (T) and fixed point properties for Lie groups
• Noncommutative \(L^{p}\)-spaces without the completely bounded approximation property
• The Baum-Connes conjecture with coefficients for hyperbolic groups
• Inequalities for Jacobi polynomials
• Zimmer's conjecture for actions of \(\mathrm{SL}(m,\mathbb{Z})\)
• A reinforcement of property (T)
• Isometric group actions on Banach spaces and representations vanishing at infinity
• Kazhdan and Haagerup properties from the median viewpoint.
• B(H) does not have the approximation property
• A Hausdorff-Young inequality for B-convex Banach spaces
• Non-Abelian harmonic analysis. Applications of \(SL(2,{\mathbb{R}})\)
• Minkowski spaces with extremal distance from the Euclidean space
• An example of a non nuclear C*-algebra, which has the metric approximation property
• Bivariant \(K\)-theory for Banach algebras and the Baum-Connes conjecture
• Random groups, random graphs and eigenvalues of \(p\)-Laplacians
• Approximation properties for noncommutative \(L^p\)-spaces of high rank lattices and nonembeddability of expanders
• Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one
• Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants
• Simple Lie groups without the approximation property
• Fixed-point spectrum for group actions by affine isometries on \(L_p\)-spaces
• Banach space actions and \(L^2\)-spectral gap
• Fourier multipliers in \(\mathrm{SL}_n(\mathbb{R})\)
• Nonlinear spectral calculus and super-expanders
• Kazhdan projections, random walks and ergodic theorems
• Strong property (T) for higher rank lattices
• A local characterization of Kazhdan projections and applications
• Property \((T)\) and rigidity for actions on Banach spaces
• The \(p\)-approximation property for simple Lie groups with finite center
• Hyperbolic groups admit proper affine isometric actions on \(l^p\)-spaces
• Connection of the dual space of a group with the structure of its closed subgroups
• A counterexample to the approximation problem in Banach spaces
• Simple Lie groups without the Approximation Property II
• Group C*-algebras without the completely bounded approximation property
• Schur and Fourier multipliers of an amenable group acting on non-commutative 𝐿^{𝑝}-spaces
• Transfer of Fourier Multipliers into Schur Multipliers and Sumsets in a Discrete Group
• NONCOMMUTATIVE DE LEEUW THEOREMS
• Strong property (T) for higher-rank simple Lie groups: Figure 1.
• PROPRIÉTÉ (T) RENFORCÉE BANACHIQUE ET TRANSFORMATION DE FOURIER RAPIDE
• Multipliers of the Fourier Algebras of Some Simple Lie Groups and Their Discrete Subgroups
• Positive Definite Bounded Matrices and a Characterization of Amenable Groups
• Approximation Properties for Group C∗-Algebras and Group Von Neumann Algebras
• Strong Banach property (T) for simple algebraic groups of higher rank
• Produits tensoriels topologiques et espaces nucléaires

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