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In this paper and its companion [31], we introduce new techniques and results in an attempt
to extend rigidity theory beyond the scope of linear groups. Amongst our main tools is the …

Several well-known open questions (such as: are all groups sofic/hyperlinear?) have a
common form: can all groups be approximated by asymptotic homomorphisms into the …

Buildings were created by Tits. They serve as a vehicle for understanding real semi-simple
groups and their p-adic analogs. These are undoubtedly the two most interesting cases, but …

In the mid 60's, D. Kazhdan defined his Property (T) for locally compact groups and used it
as a tool to demonstrate that a large class of lattices are finitely generated. Recall that a …

Let be a Kac–Moody Lie algebra. We give an interpretation of Tits' associated group functor
using representation theory of and we construct a locally compact" Kac–Moody group" G …

We present the surge of activity since 2005, around what we call the algebraic (as
contrasted with the geometric) approach to Kazhdan's property (T). The discussion includes …

It is well known that the spectral gap of the down-up walk over an $ n $-partite simplicial
complex (also known as Glauber dynamics) cannot be better than $ O (1/n) $ due to natural …

Garland's method with Banach coefficients Page 1 ANALYSIS & PDE msp Volume 16 No. 3
2023 IZHAR OPPENHEIM GARLAND’S METHOD WITH BANACH COEFFICIENTS Page 2 …

Vanishing of cohomology and property (T) Page 1 Groups Geom. Dyn. 9 (2015), 67–101 DOI
10.4171/GGD/306 Groups, Geometry, and Dynamics © European Mathematical Society …