Related papers: IP-rigidity and eigenvalue groups

In this paper we introduce and explore the notion of rigidity group, associated with a collection of finitely many sequences, and show that this concept has many, somewhat surprising characterizations of algebraic, spectral, and unitary…

By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d.\ sequences. This observation not only explains the remarkable properties of lacunary trigonometric…

We define a class of discrete abelian group extensions of rank-one transformations and establish necessary and sufficient conditions for these extensions to be power weakly mixing. We show that all members of this class are multiply…

Let $G$ be a virtually special group. Then the residual finiteness growth of $G$ is at most linear. This result cannot be found by embedding $G$ into a special linear group. Indeed, the special linear group $\text{SL}_k(\mathbb{Z})$, for $k…

We define the topological complexity sequence of a group as the sequence of topological complexities of its Milnor constructions. This sequence may be regarded as an intrinsic refinement of the topological complexity of a group and, unlike…

Connections between longest increasing subsequences in random permutations and eigenvalues of random matrices with complex entries have been intensely studied. This note applies properties of random elements of the finite general linear…

We introduce a subclass of linear recurrence sequences which we call poly-rational sequences because they are denoted by rational expressions closed under sum and product. We show that this class is robust by giving several…

We study the ISR (von Neumann invariant subalgebra rigidity) property for certain discrete groups arising as semidirect products from algebraic actions on certain 2-torsion groups, mostly arising as direct products of $\mathbb{Z}_2$. We…

We prove that a class of infinite measure preserving transformations, satisfying a "strong" weak mixing condition, generates all rigidity sequences of all conservative ergodic invertible measure preserving transformations defined on a…

The article establishes a long list of rigidity properties of lattices in G = SO(n,1) with n>=3 and G = SU(n,1) with n>=2 that are analogous to superrigidity of lattices in higher-rank Lie groups. The arguments are set in the context of…

We consider the group property of being icc. We give several examples of icc groups and study its stability under usual algebraic constructions.

For a compact metric space $X$ with a group $G$ acting on it continuously, an invariant random compact is a Borel probability measure on the space of nonempty compact subsets of $X$ that is invariant under the action of $G$. The action is…

We show that the class $\mathscr{B}$, of discrete groups which satisfy the conclusion of Popa's Cocycle Superrigidity Theorem for Bernoulli actions, is invariant under measure equivalence. We generalize this to the setting of discrete…

Given a fixed prime number \(p\), the multiplet of abelian type invariants of the \(p\)-class groups of all unramified cyclic degree \(p\) extensions of a number field \(K\) is called its IPAD (index-\(p\) abelianization data). These…

The focus of this paper is the phenomenon of rigidity for measure-preserving actions of countable discrete abelian groups and its interactions with weak mixing and recurrence. We prove that results about $\mathbb{Z}$-actions extend to this…

By studying the commuting graphs of conjugacy classes of the sequence of Heisenberg groups $H_{2n+1}(p)$ and their limit $H_\infty(p)$ we find pseudo-random behavior (and the random graph in the limiting case). This makes a nice case study…

We survey some of the progress made recently in the classification of von Neumann algebras arising from countable groups and their measure preserving actions on probability spaces. We emphasize results which provide classes of…

We study the relationships between three different classes of sequences (or sets) of integers, namely rigidity sequences, Kazhdan sequences (or sets) and nullpotent sequences. We prove that rigidity sequences are non-Kazhdan and nullpotent,…

For any infinite zero-density integer set M, we found a rigid measure-preserving transformation mixing along M by answering Bergelson's question. Gaussian and Poisson suspensions over infinite constructions are suggested as suitable…

We survey some recent developments and applications of the study of the rigidity properties of natural algebraic actions of multidimensional abelian groups.