We discuss special properties of the spaces of characters and positive definite functions, as
well as their associated dynamics, for arithmetic groups of product type. Axiomatizing these …

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Let Γ be a lattice in SO_0(n,1). We prove that if the associated locally symmetric space
contains infinitely many maximal totally geodesic subspaces of dimension at least 2, then Γ …

Let G be a higher rank semisimple linear algebraic group over a non-Archimedean local
field. The simplicial complexes corresponding to any sequence of pairwise non-conjugate …

Abstract The Prouhet-Thue-Morse sequence and its generalizations have occured in many
settings.''Morse-Kakutani flow''refers to Kakutani's 1967 generalization of the Morse minimal …

We introduce a class of countable groups by some abstract group-theoretic conditions. This
class includes linear groups with finite amenable radical and finitely generated residually …

We prove that a large family of higher rank simple Lie groups (including SL n (R) for n≥ 3)
and their lattices have Banach property (T) with respect to all super-reflexive Banach …

This book is concerned with analytic approaches of studying groups and their actions. Much
attention is devoted to the study of amenability and Kazhdan's property (T), which are …

Let C→ be a category whose objects are semigroups with topology and morphisms are
closed semigroup relations, in particular, continuous homomorphisms. An object X of the …

We establish vanishing results for limits of characters in various discrete groups, most
notably irreducible lattices in higher rank semisimple Lie groups. This is achieved by …