Related papers: Superrigidity for irreducible lattices and geometr…

For geometrically finite group actions on hyperbolic metric spaces and under certain assumptions on the growth of parabolic subgroups, we prove a global shadow lemma for Patterson-Sullivan measures, as well as a Dirichlet-type theorem and a…

We give very precise bounds for the congruence subgroup growth of arithmetic groups. This allows us to determine the subgroup growth of irreducible lattices of semisimple Lie groups. In the most general case our results depend on the…

We describe a natural generalization of irreducibility in order lattices with arbitrary metrics. We analyse the special cases of valuation metrics and more general metrics for lattices. This article is mainly based on a part of the author's…

This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…

The purpose of this paper is to give an application of the gluing theorem for special Lagrangian submanifolds of a Calabi-Yau 3-fold. We proved a gluing theorem before to smooth a codimension-two singularity of a particular special…

Margulis showed that "most" arithmetic groups are superrigid. Platonov conjectured, conversely, that finitely generated linear groups which are superrigid must be of "arithmetic type." We construct counterexamples to Platonov's Conjecture.

Discretization of supersymmetric theories is an old problem in lattice field theory. It has resisted solution until quite recently when new ideas drawn from orbifold constructions and topological field theory have been brought to bear on…

We extend the polydisk theorem of [21], originally established for classical Cartan-Hartogs domains, to Hartogs domains over arbitrary (possibly reducible and exceptional) bounded symmetric domains. We further establish a dual counterpart…

We show that most homogeneous Anosov actions of higher rank Abelian groups are locally smoothly rigid (up to an automorphism). This result is the main part in the proof of local smooth rigidity for two very different types of algebraic…

New series of $2^{2m}$-dimensional universally strongly perfect lattices $\Lambda_I $ and $\Gamma_J $ are constructed with $$2BW_{2m} ^{\#} \subseteq \Gamma _J \subseteq BW_{2m} \subseteq \Lambda _I \subseteq BW _{2m}^{\#} .$$ The lattices…

We systematically investigate cocycle superrigidity in the setting of finite rank median spaces for product groups and Kazhdan groups. By employing a dynamical approach to superrigidity, we establish, for a median space X of finite rank,…

We describe the absolute retracts for the following classes of finite lattices: (1) slim semimodular lattices, (2) finite distributive lattices, and for each positive integer $n$, (3) at most $n$-dimensional finite distributive lattices.…

In this paper, we prove a rigidity theorem for smooth strictly convex domains in Euclidean spaces.

In this paper we study the property of generic global rigidity for frameworks of graphs embedded in d-dimensional complex space and in a d-dimensional pseudo-Euclidean space ($R^d$ with a metric of indefinite signature). We show that a…

We prove a gap rigidity theorem for diagonal curves in irreducible compact Hermitian symmetric spaces of tube type, which is a dual analogy to a theorem obtained by Mok in noncompact case. Motivated by the proof we give a theorem on weaker…

We single out a notion of staticity which applies to any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For (time-symmetric) initial data sets modeled at infinity on any of these latter examples,…

Let $k$ be a perfect field of characteristic $p \geq 3$, and let $K$ be a finite totally ramified extension of $K_0 = W(k)[p^{-1}]$. Let $L_0$ be a complete discrete valuation field over $K_0$ whose residue field has a finite $p$-basis, and…

We consider five dimensional theories compactified on the orbifold S^1/Z_2 and prove that spontaneous local supersymmetry breaking by Wilson lines and by the Scherk-Schwarz mechanism are equivalent. Wilson breaking is triggered by the…

Let $G$ be a non-compact semisimple Lie group with finite centre and finitely many components. We show that any finitely generated group $\Gamma$ which is quasi-isometric to an irreducible lattice in $G$ has the $R_\infty$-property, namely,…

Let $G$ be a real reductive Lie group, $L$ a compact subgroup, and $\pi$ an irreducible admissible representation of $G$. In this article we prove a necessary and sufficient condition for the finiteness of the multiplicities of $L$-types…