Related papers: A rigidity result for normalized subfactors

We say that a countable discrete group $\Gamma$ satisfies the invariant von Neumann subalgebras rigidity (ISR) property if every $\Gamma$- invariant von Neumann subalgebra $\mathcal{M}$ in $L(\Gamma)$ is of the form $L(\Lambda)$ for some…

We demonstrate quasi-isometric rigidity for the product of a non-uniform rank one lattice and a nilpotent lattice. Specifically, we show that any finitely-generated group quasi-isometric to such a product is, up to finite noise, an…

Let $\C(\Gamma)$ be the set of isomorphism classes of the finite groups that are homomorphic images of $\Gamma$. We investigate the extent to which $\C(\Gamma)$ determines $\Gamma$ when $\Gamma$ is a group of geometric interest. If…

Every homomorphism from finite index subgroups of a universal lattices to mapping class groups of orientable surfaces (possibly with punctures), or to outer automorphism groups of finitely generated nonabelian free groups must have finite…

In this paper we study the bi-Lipschitz triviality of deformations of an analytic function germ $f$ defined on a germ of an analytic variety $(X, 0)$ in $\mathbb C^n$. We introduce the notion of strongly rational $\mathscr R_X$-bi-Lipschitz…

We rigorously derive linear elasticity as a low energy limit of pure traction nonlinear elasticity. Unlike previous results, we do not impose any restrictive assumptions on the forces, and obtain a full $\Gamma$-convergence result. The…

We prove for a $\Theta-$positive representation from a discrete subgroup $\Gamma\subset \mathsf{PSL}(2,\mathbb{R})$, the critical exponent for any $\alpha\in \Theta$ is not greater than one. When $\Gamma$ is geometrically finite, the…

A discrete group which admits a faithful, finite dimensional, linear representation over a field $\mathbb F$ of characteristic zero is called linear. This note combines the natural structure of semi-direct products with work of A. Lubotzky…

We introduce a new canonical form of lattices called the systematic normal form (SNF). We show that for every lattice there is an efficiently computable "nearby" SNF lattice, such that for any lattice one can solve lattice problems on its…

We give a simple algorithm that enables us to determine whether a subgroup of finite index of the Hecke group is normal.

Let G be a real semisimple Lie group with no compact factors and finite centre, and let $\Lambda$ be a lattice in G. Suppose that there exists a homomorphism from $\Lambda$ to the outer automorphism group of a right-angled Artin group…

Let $\Gamma$ be a discrete group with property $(T)$ of Kazhdan. We prove that any Riemannian isometric action of $\Gamma$ on a compact manifold $X$ is locally rigid. We also prove a more general foliated version of this result. The…

Let $G$ be a connected semisimple real algebraic group and $\Gamma<G$ be its Zariski dense discrete subgroup. We prove that if $\Gamma\backslash G$ admits any finite Bowen-Margulis-Sullivan measure, then $\Gamma$ is virtually a product of…

We prove that every finitely generated, residually finite group $G$ embeds into a finitely generated perfect branch group $\Gamma$ such that many properties of $G$ are preserved under this embedding. Among those are the properties of being…

Let $\Gamma$ be a group acting on a scheme $X$ and on a Lie superalgebra $\mathfrak{g}$, both defined over an algebraically closed field of characteristic zero $\Bbbk$. The corresponding equivariant map superalgebra $M(\mathfrak{g},…

Let $\Gamma$ be an irreducible lattice in a product of n infinite irreducible complete Kac-Moody groups of simply laced type over finite fields. We show that if n is at least 3, then each Kac-Moody groups is in fact a simple algebraic group…

We show that the subgroup lattice of any finite group satisfies Frankl's Union-Closed Conjecture. We show the same for all lattices with a modular coatom, a family which includes all supersolvable and dually semimodular lattices. A common…

Let $G$ be a finite insoluble group with soluble radical $ R(G)$. The solubility graph $\Gamma_{\rm S}(G)$ of $G$ is a simple graph whose vertices are the elements of $G\setminus R(G) $ and two distinct vertices $x$ and $y$ are adjacent if…

The main result of this paper is a probabilistic construction of finite rigid structures. It yields a finitely axiomatizable class of finite rigid structures where no L^omega_{infty, omega} formula with counting quantifiers defines a linear…

Let $G$ be an almost simple, simply connected algebraic group defined over a number field $k$, and let $S$ be a finite set of places of $k$ including all infinite places. Let $X$ be the product over $v\in S$ of the symmetric spaces…